Good morning/afternoon/evening, Codeforcers!

We (Nezzar, triple__a, Nanako) are very excited to present to you Codeforces Round 698 (Div. 1) and Codeforces Round 698 (Div. 2), which will take place in 28.01.2021 17:35 (Московское время).

There will be **6 tasks** waiting for you to be solved in **135 minutes**!

We would also want to thank:

isaf27 for the coordination and discussion of this round!

KAN for great help and advice of round prepartion!

alex20030190, KAN, Roundgod, gisp_zjz, sshwyR, Retired_xryjr233, jhdonghj112, low_, dragon_bra, gamegame, mmello, cycl, Reiva5, kzyKT, hitonanode, parker0523, hieplpvip for testing and providing valuable feedback of the problems!

MikeMirzayanov for great systems Codeforces and Polygon!

Score distribution will be announced at $$$n$$$ $$$(0 \leq n < + \infty)$$$ minutes before round starts.

We hope you high performance with a lot of points earned during contest!

**UPD1** $$$n$$$ is chosen to be $$$300$$$.

Score distribution is

**Div. 2**: 500-1000-1500-1500-2000-2500

**Div. 1**: 500-1000-1500-2250-2750-4000

**UPD2** The contest is ended despite CodeForces under attack from DDoS midway. Thanks all for joining!

Here is the editorial: Editorial

**UPD3**

Congratulations to the winners!

Div 1:

div 2:

People who were first to solve each task:

D2A: pj423

D2B: Zeyush

D2C: BelieveInYou

D2D/D1A: IgorI

D2E/D1B: SSRS_

D2F/D1C: Benq

D1D: Um_nik

D1E: tourist

D1F: boboniu

As an author...

Next time just try to say "As an" and look how many contribution you get

As an

well we learned its a good idea :)

(when i wrote that comment 1-gon’s comment had negative contribution)

And now let other colors try the same.

As another color, give me contribution

Are we going to have all the colors sorted in descending order? I am waiting...

As another color, give me contribution

As the same color.... welll...

An Ass

Ann's ass

Thankyou for the contest :)

To be honest triple__a worked very hard for this contest and I am more on a supportive role, so he should receive more contribution than me xd

As a participant...

your comment has your name.... triple_a ("As An Author")

my first comment

As an Um_nik, ***** div1A.

As a 17:35 msk hater...

missing

almost-copy-pasted-partlmaoSetters and testers from Hong Kong :o

Wait Nezzar are you RB the villager? (pls don't ghost me)

what is rb the villager???

Not really sure what "the villager" mean here xd (well I admit I knew what RB means...)

^because of privacy issues I removed the face

My first round after a long pause. Wish all participants good luck and easy problems

Hope it remains rated.

Um contest tab shows 120 minutes but you said 135 minutes?

Nice catch! The one in contest tab will be changed to 135 minutes.

Please give me 100 points for successful hacking attempt in this round. Thanks.

How much delay this time?

n minutes (0 <= n <= +inf)

0<= n

<+infNice;)

A question regarding the constraints of n:

Shouldn't it be $$$(0 \leq n < + \infty)$$$ instead of $$$(0 \leq n \leq + \infty)$$$?

Sure thing

Infinite thanks

Does this mean that:

We can actually make the constraints better. Since we will anyways get the scoring distribution after this certain point of time the range of $$$n$$$ can be better written as $$$0 \le n \le f$$$ where $$$f$$$ is a finite number which I don't have the finiteness to calculate.(but it is finite).

Auto comment: topic has been updated by Nezzar (previous revision, new revision, compare).As a Japanese participant, I was amazed that there is another p*0523 near Japanese testers in the post...!

It's comforting to know that $$$n \ge 0$$$.

Thanks for the contest Nezzar, I am a beginner and I managed to solved three questions in the previous contest, really hyped, looking forward to this one too... Love you codeforces Family!!!

Long time no see (div1)

finally div1! ^_^

As a tester...

Hope this round will go smoothly!

Oh, my fault. Thank you! I will fix it!

Let's hope that

MikeMirzayanovdoes not have any doctor's appointment scheduled for Thursday.I have noticed that there are no weekend contests?

Thank you triple__a, Nezzar and Nanako for preparing div.1 and div.2 contests.

Just going to say that I'm a huge fan of starting round announcements with a "Good Morning!"

.

As a co-author...

Maybe I don't really deserve this appellation... I think I'm more like a tester because triple_a and Nezzar come up with many ideas with great inspiration when I just come up with much less ideas (and finally none of mine is interesting enough to become a problem in this round lul).

triple_a and Nezzar is really respectable. They spend half a year preparing this round. Comparing with them, I think I just do something that's not worth much mentioning.

Hope you can have fun in this round!

I am sure all of you work very hard and prepare such contests. Thank you for all the efforts you put!

I can understand you. Different coordinators have different review standards. Some coordinators are very strict, and they have a very low pass rate for the questions they review. This does not mean that your topic is not interesting enough, maybe it is just that the level of interestingness does not meet the standards of this coordinator. Different coordinators have different definitions of interesting, so your topic does not seem interesting enough for this coordinator, but another coordinator (possibly) will find your topic interesting. Then, even if your topic is not selected, I think your contribution is enough to make us thank you. Looking forward to solving the problem of your proposition, although my level is not high, I will try my best.(One more thing to say, if your dream is to be an excellent writer, don't be disappointed in yourself. I believe that one day, you can impress the coordinator with your interesting topic.)

Thankyou for the contest :)

n can be equal to 0 as well, then scoring distribution may be known only when the contest starts? :(

It would be interesting if n <= -135

Another China round! Thank you very much for the selfless dedication of the authors and testers, so that we can have a different experience. Then, let me guess, after this round, another China round is coming soon? (maybe the global round)? Let me look forward to it^__^

As a tester, hopefully you also find the problems are interesting like I do! I enjoy testing the problem set even I test it after tiring work. Good luck all!

Why can't users with a $$$1900 \leq rating < 2100$$$ register for the Div. 2?

In every Div1 + Div2 round, Candidate Masters are considered Div1 participants.

Codeforces Declares round unrated due to long queues.

Meanwhile CodechefNo problem, just extend the round by 30 mins

Notice the unusual solving time (135 mins).

Finally a div1 round!

could've easily had a tighter bound for n(the total no. of mins before the round starts)

Oh well...

17:35(UTC)=22:35(UTC+8)=less sleep

Since when $$$17.35 \text{ (UTC)} = 22.35 \text{ (UTC+8)}$$$ :( ? Did you mean $$$17.35 \textbf{ (MSK)}$$$?

My question is in this solution 105544722 return me answer please

VOT ETO DAAAAAAAA

135 minutes! It is interesting.

Long queue or something IDK, but I hope it does not happen :D

long queues started even before the beginning of the contest

`Score distribution will be announced at n (0 ≤ n < +∞) minutes before round starts.`

Does this mean it is possible it will not be included in blog before contest, rather we will be seeing the distribution in contest?

Well DIv2 D = DIv1 A with this score distribution right!

Nezzar Please remove "!" from 300, it seems like you want to say 300 factorial :(

Thanks for replacing "!" with "."

I suggest holding a testing contest before today's contest to test the In queue, MikeMirzayanov!

$$$4000$$$ points for Div.1 F...That's gonna be tough.

they said that it took half-year preparing it so they had put a lot of effort to make it. so I think why problem F gives 4000 points and I think div2 will have a subproblem.

u r right

I hope I can solve problem D in this contest.

Good luck

Good luck!

Interesting score distribution for Problem C and D.. :)

Fortunately the wait for div1 + div2 is over

oh！Good luck！

im the first upvote of your first comment :dab:

Hoping a good contest today without any queue issues :)

contest getting delayed in 1....

This is the joke about the hard contest you are looking for

I am facing queue issues on Problem B

Is there someone else also ?

Edit: Resolved

Yes, the queue is very large. I hope it will be fixed soon.

YES_NO-forces :D

Whoever came up with the problems really overestimates the CF community.

Jokes aside, a tough one for sure.

Hello Community. I want to ask one question. I submitted B problem twice, both passed pretests. Which one will be considered ? My rank went from 2200 to 4400 . Please somebody tell me .

The latest submission is considered.

I submitted first at 44 minutes and second at 1hr 2 min. So, the solution with 1hr 2min will be considered?

yes as that is your latest submission

My disappointment is immeasurable and my day is ruined.

Luckily the day is over. Practice for the next one!

Yes Buddy, atleast today I learned something new :p .

Very nice problem set... thank you authors

Can someone help me with the 2nd one after the contest?

How to solve C?

suppose n = 3 , then suppose array a will be of form $$$a_1<a_2<a_3$$$ and their negative values also . Then array d in increasing order will be (note that every number in d will be repeated twice so we are only considering n numbers) say $$$d_1<d_2<d_3$$$ then $$$2*(a_1+a_2+a_3) = d_1$$$ , $$$4*a_2 + 2*a_3 = d_2$$$ , $$$6*a_3 = d_3$$$ .You can show this by using formula in question. Now you can find $$$a_3,a_2,a_1$$$ one after the other using the equations .

Similar generalization for any n.

i probably overkilled C, but was there a reason for why the numbers were distinct? it cost me a WA coz I didn't think they should be, probably why my solution was hard.

Exactly, there was no need of them to be distinct.

to exclude 0 I think

$$$0 = -0$$$ is true.

Yes => 0 cant be a number in the initial array (a)

There is a need for the values to be distinct because if you consider the array a = [-1 1 3 -3 -3 -3], you get the consequent d array to be [12 16 24 12 12 12], and therefore, a lot of useful properties fundamental for the original problem wouldn't be there.

oh yeah got it

A big big dislike for Div2 C and D. Both are more christmas riddles than programming problems. I do not care any more for orginal ideas or the like. For me this kind of riddles are only boring. You need to find some wired observation, like walking blind in a labyrinth finding the exit.

totally agree, id rather have repetitive algorithmic problems than these find the pattern after 100 examples problems.

Ya I don't know who likes these problems if most of them diskikes this type of problems then these puzzles are made for whom a big question mark on the community?

I like them, and I know some others who do. More math-minded people I think tend to enjoy them

It is not atcoder no!

I think div2D/1A was a great problem. It was refreshing to see Bezout's Theorem, and it was a cute observation.

Div 1B on the other hand was just standard lazy seg-tree so that wasn't so exciting but it was cool still.

How to solve Div1C?

If such things are cute for you ;)

I liked the segment tree, the update operation was not very intuitive for me, I think I never implemented that kind of update before.

I don't have any ideas about D, but I think the observation for C was not hard to stumble upon. I would say C was more intuitive and easier for me than B.

Basically, take some small arrays, then try writing the sum of absolute difference for them, the way it's defined — but don't calculate the value, instead just observe the terms themselves in the sum of absolute difference.

Yes, and some hundred participants did like this. Some other thousends did not. So where is the point?

It was easy for you, so it is a good problem?

It was hard for you, so is it a bad problem?

I think if one were to try out small arrays and try to observe from them, the observation itself is not a very obscure pattern.

But yes, I get your point. I am not saying it was a great problem — but was one of the better problems compared to other Div2 contests these days.

For C i solved by using the definition of how array d is constructed (by getting n equations).So it wasn't puzzle for sure.

In D i observed (don't know if correct) that we require at most 2 numbers to create k .

In B , i had idea that after a point all numbers can be created by lucky numbers but was not able prove it and didn't solved it.

So i can't say anything regarding D and B.

Let's hope tomorrows Educational round will be a good one.

I disagree with you . They were really beautiful problem with some really good observation . I couldn't solve D but you can see my solution to C which is I think really clean and nice .

These day if you want to get good in codeforces contest then it appears practicing puzzles is more beneficial than studying algorithms to

agreed. Solving C was not at all fun. it was just some boring observations.

Well, here is how you could navigate a labyrinth even blind without any weird observations or luck: click

How to solve B and in problem D do we needed to check if k can be formed by any two numbers in array ?

for problem B, you can use lucky number multiple times. means for d= 7, ai = 52, 7+7+7+7+7+17 is allowed answer

You can compute all lucky smaller than d * 10. If the current number is >= d * 10, print "Yes. Else if it is among the previously calculated numbers print "YES". Else print "NO"

why num>=10*d is always YES.

Because no matter how much you subtract 7 from the number you get to a number that starts with 7 (70, 71,.., 79)

In problem B, we need to observe that for every number greater than 10*d, it is always possible to get the sum, for number < 10*d we can brute force and check.

and that observation I made by running a dp solution up to some small numbers for each digit. I saw that beyond 10*d everything was possible. I could not prove this and continued with this observation.

dp solutionchc simply checks if the number contains d as digit.

the simple proof of this is lets say a number is >= 10 * d then 10 * d would be of form "d0" then the remaining n % d part can be added to this number and still you have a digit 'd' on the tens place.

Thanks

how to do D?

Nezzar's favourite jumpshttps://www.youtube.com/watch?v=ESnIx0lvjAs&t=62s

pp maps :(

plz enjoy game

Can someone please give a test-case for which my code fails for problem C? WA_CODE

The result of formula should not repeat and should not be negative.

Any hints for D?

You can view the operation as taking a number in the array and adding the difference (with your choice of sign) between any two other numbers of the array to it. Note that you can repeat the operation as many times as you want.

Assume we have set $$$(a_{1}, \dots a_{n})$$$ and $$$g=gcd(a_{2}-a_{1}, \dots , a_{n}-a_{n-1})$$$. Then the closure of operation $$$2x-y$$$ is set $$$(\dots a_{1}-g, a_{1}, a_{1}+g, a_{1}+2g, \dots)$$$.

Could you explain what is closure, seems interesting!!!

Assume we have a set $$$S$$$ and operation "bring some numbers $$$a, b, \dots$$$, and insert into $$$S$$$ some value $$$f(a, b, \dots)$$$". Let do operation while we can get number, which is not in $$$S$$$. The set we got is called closure of set above operation (I am not sure if I wrote it correctly in english). It is just definition.

Ohh nice, got it thanks for explaining

So Div1B/Div2E isn't segment tree or what?

I solved it using segment tree, don't know if there's an easier solution

Yes, it was segtree with: "set all values in a range to $$$x$$$ " and "find sum of a range".

Yes, you consider the queries in reverse order, and then note that the starting string is uniquely determined by the conditions (if at a point you have exactly half the elements in a range to be 0 and the other half to be 1, then this is invalid, and the answer is NO, otherwise you can just set the whole range to the majority element of the range). If the array so found is the same as the given initial array, then the answer is YES, else it's NO.

Exactly did this but probably there is sum bug in my code :(

not exactly, After doing this i tried to change the array so that is the wrong logic :(

I personally did a sum-query for each element (in the form [l, r] = [i, i]) to retrieve the new array using these operations, so this might be useful if you can afford to take $$$O(n \log n)$$$ time for creating the final array.

both segment tree and chtholly tree is ok

Is there anyone who also got WA on pretest 7 in Problem C.

Very disappointing problem c :(

Assuming we did the same thing, i.e. creating the sorted positive half of array a, I was getting it when I was checking if the array is non-decreasing, it was resolved when I checked the array to be strictly increasing.

In div 2D, If we can form any two consecutive numbers, we can form any number. Was this observation helpful?

Very close, but no. The observation that works is that if you take the difference of all elements with the first element, and call the resulting array $$$b_1, \dots, b_{n - 1}$$$, then performing the operation corresponds to finding the sum/difference of a few of these elements, and you can find an operation where it corresponds to finding the sum/difference of any two elements of $$$b_i$$$. Hence, the gcd of all $$$b_i$$$'s is achievable, and this is necessary and sufficient.

https://acm.timus.ru/problem.aspx?space=1&num=1578&locale=en

deleted

Problems have been repeated many times in the past, verbatim. While the organizers try to avoid this, this doesn't make the contest unrated.

deleted

We are really sorry that D1C has been appeared before. None of the team know the existence of this problem and we come up the whole problem ourselves (the idea comes from the lore actually)

it's ok , i am not blaming you, i know it;s impossible to remember all the problems

When you use

`double`

to get the distance of two points with fuction`sqrt`

in div.1C:upd: WHY IT CAN PASS THE SYSTEM TEST? Too weak tests >_<

Hack case:`As a low-ranking coder in this round, I hope I can get some upvotes.`

F looks beautiful, but I have no idea how to solve it :<. After solving some differential equation I managed to understand first sample, but that doesn't generalize at all to almost any other inputs xd

This paper explains how to count the probability that the maximum part is <=k after picking n random points. Then we need to put those probabilities into an exponential generating function, it turns out to be a sum of O(len) terms of form koef*exp(alpha*x)*x^beta for alpha of form i/total_length and beta up to total_length, so there are O(total_length^2) possible terms up to koef. Then we need to multiply all those generating functions, which boboniu does in O(total_length^3) by just using the fact that each of the functions has only O(len) nonzero terms so we can multiply naively, but maybe some FFT was required? The system test will tell :)

Getting all details right within the contest is insane, hats off to boboniu!

The editorial says that we actually have only O(n*total_length) nonzero terms in the product, therefore the naive multiplication is O(n*total_length^2) which should be good.

Such an awful and terrible and unfair contest

Why? Was there some issue in Div 2?

I do not see how it was unfair.

Having more math elements in a contest isn't unfair to anyone. As long as the everybody can login at the same time, and the problems are correct, there is never an unfair contest. There may be "unbalanced" contest sometimes, but not this one. It isn't the author's fault if the problems had troubled you.

Chinese contests are even more faulty than Chinese goods.

For everyone who got WA on test 2, Div1B/Div2E, try this case:

2 1

11

10

1 2

The correct output is "NO", and if your output is "YES", you probably forgot that

strictly lessthan half of the interval can be changed (at least that was my bug)4/6 problems in div2(BCDE) just required me to output yes/no! I was grateful for not asking me to construct a way or something lol

Thanks for strong pretests for A and B....i loved to solve those....But couldn't even understand C

Please next time don't give us riddles like C or D, we all want programming problems!

What was the problem? I think they were perfectly fine problems.

After countless attempts and failing on B, losing 150 points and going down to 1500 from 1770 in just 2 contests, I've found a solution to the extended version of B.

So in case anybody is curious, suppose that the question also asked for example numbers, not just a "YES" or "NO".

We can see that number X * d, can be expressed as sum of X d's, in form:

d d d .... d (X times)

In other case, we can take a look at the number's last digit (say P) ans find the minimum multiple of d which corresponds to the same last digit. So suppose we have input:

113 7

The output should look like:

7 7 7 7 7 7 7 7 57

And how do we get this? Simply, if the multiple that corresponds to our last digit is equal to X * d, then we can take d and print it (X — 1) times and finally print S — (X — 1) * d, where S is the starting number.

The only case when it is impossible to print a valid sequence is when the lowest multiple with the same last digit is greater than our current number.

I hope some of you found this interesting, as it can be made into a solution to the easier version of the problem.

EDIT: And this goes to prove why 25 isn't possible, 53 isn't possible, 46 isn't possible, etc.

4 of the first 5 problems of Div2 were

YES/NOproblems. Maybe author's crush is very straightforward. Accpet or Reject his proposal inYES/NOIn div1 C, is the answer always possible?

yes

As an

Welcome to MathForces

true XD

I thought it was only me XD

I did 2 mistakes. First < and second not reading distinct :'(

Auto comment: topic has been updated by Nezzar (previous revision, new revision, compare).Who else got screwed in that contest? Though problem set was nice.

Thanks for contest! C was very nice to solve.

Can you explain the idea? I tried reverse the array A, but it seems the wrong.

I will give you an example to think about the idea. Let's say we have 3 distinct numbers (we will use the positive numbers since it is easier to reason about) [a, b, c] where a > b > c.

Calculating the sum of differences for a:

In general, with [a_1, ... , a_n], where a_1 > a_2 > .. > a_n, then sum of differences for a_1 is as follows:

From this, you can find the value of a_1. Next, the way I thought about it was to consider [a_2, ..., a_n] (i.e. disregard a_1). But one thing is sum of differences for a_2 would be subtracted by 2a_1. This is because there is a term in the original sum of differences for a_2 (which includes a_1):

since we are disregarding a_1, we should subtract it by 2a_1.

After subtracting, just do the same method as before to find a_2, then just do it until a_n.

Hope this helps bro. Took me awhile to figure out.

I'd like to ask

After I had passed the questions in the contest

Again, I submit the approved code for this topic

Why is the second pass time calculated

105770938 In B, why I am getting wrong at test case 2 ?

d = 2, a = 21

My code give "NO" output

What is the solution if "YES"

when d = 2, 21 itself is a lucky number :)

Auto comment: topic has been updated by Nezzar (previous revision, new revision, compare).it seems they didn't put the most basic case on problem C 1 1 0 0

In the problem Div2(B), What was the case for which most of the submissions got Wrong Answer on Test Case 2 in 10021th Token??

d=2 and a_i=21, which should be YES.

What about 10031st? Upd: Nvm got it.

No shade on the writers, the problems were very cool and clever. These kind of ad-hoc, constructive problems help with developing quick thinking and problem solving skills. And they are great in a contest as long as there's diversification in the problems. Or atleast 2 out of 5 contests focus on DSA skills too.

Majority of participants are here to improve their DS&A skills (by majority I mean people who don't have high ratings and aren't seasoned programmers). I would love to solve some questions on tree algorithms, dp, binary search, dsu or any basic/advanced algorithm once in a while to develop those skills too. I understand this might not be the priority for some participants, but this would help us keep in touch with actual data structures and algorithms.

Here is a blog (Changes in Codeforces problem style over 2020) where this issue is very well put.

PS — Using an alternate ID. Please read before downvoting. Thanks

Okay, let me repeat.

1) If you want to solve standard problems on tree/dp/dsu/e. t.c, then you can find it in any archive, you do not need to solve it during a real contest if you want to practice this topics.

2) If you want to solve a non-standard problem using any algorithm at a contest, this is fine, but

2.1) Such problems are almost always more difficult than Div2D, because otherwise required algorithm is much harder than problem itself

2.2) it is very difficult to come up with a high-quality problem on a well-known topic (atleast for me :D)

if my code wasn't optimized enough to pass the system test why did it pass pretests? Come on Codeforces, what's the problem??

Dude what the heck are you saying lol

To not keep you waiting, the ratings updated preliminarily. In a few hours, I will remove cheaters and update the ratings again!

https://mirror.codeforces.com/contest/1478/submission/105734232

Nice way to escape from MOSS. Putting useless for loops!Check out my explanation of problem C — solution

what is 10013th testcase in B??

d = 2

ai = 13

can someone point out the error in my code for div2-C

## include <bits/stdc++.h>

## include

## define fio ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)

## define ll long long

## define endl "\n"

## define lb lower_bound

## define ub upper_bound

## define fo(i,a,b) for(i=a;i<b;i++)

## define all(v) (v).begin(),(v).end()

## define all1(v) (v).begin()+1,(v).end()

## define sort0(v) sort(all(v))

## define max3(a,b,c) max(max((a),(b)),(c))

## define max4(a,b,c,d) max(max((a),(b)),max((c),(d)))

## define min3(a,b,c) min(min((a),(b)),(c))

## define min4(a,b,c,d) min(min((a),(b)),max((c),(d)))

## define pb push_back

## define ppb pop_back

## define mp make_pair

## define inf 9999999999999

const ll mod=1e9+7;

ll inv(ll i){if(i==1) return 1;return (mod-((mod/i)*inv(mod%i))%mod)%mod;}

ll gcd(ll a,ll b){ if (b==0) return a;return gcd(b,a%b);}

ll pwr(ll a, ll b) {a %= mod; ll res = 1;while (b > 0) {if (b & 1) res = res * a % mod; a = a * a % mod; b >>= 1;}return res;} using namespace std;

int main() { fio; long long t; cin>>t; while(t--){ ll n,res=0,i,sum=0,max=0; cin>>n;

}

Some tags

105785851 Why does this brute force sol work for div2 B? Shouldn't this get TLE?

I think the constraint of number of test cases is saving the sol from getting TLE.

1<=t<=9

.

Oh god I just realized that tourist must be in second or first place to win some rating. That's scary...

Can somebody tell me how they got their idea of solving B, I found B really non intuitive.

I just think that

`d < 10`

so no matter what`d`

and`a`

you are working with, just minus`d`

from`a`

will give you a number with the digit in the tens (hundreds, thousands,...) place is`d`

.Can anyone explain the intuition or solution to problem D?

In the problem c , I dont know whats the tc , it'll be very helpful if someone figure outs the error ,by the way , the error that is being displayed by judge is in tc 11 (which is obviously is not visible due to its length) The code is here

Love this contest <3

for D2F(D1C), it is quite easy, easier than D2D/D2E, why it is placed in the last problem, and get so much score? my solution is, firstly generate a random permutation as initialization, then brute force search an valid permutation based on this initialization permutation. the solution is very simple and source code is very short. if i know this i will definitly finish D2F earlier than D2D/D2E.