4. Claims Processing
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

There is a pile of $$$N$$$ claims on the desk of a big boss. The claims are numbered from top to bottom from $$$1$$$ to $$$N$$$.

The boss signs the first claim and removes it from the pile, throws away the second one, and puts the third one down the pile. The process continues in this fashion until all the claims in the pile are gone.

Determine whether the claim with number $$$K$$$ will be signed or thrown away, and also the number of the step during which this will happen. One step is each of the three actions described above.

Input

The first line of the input contains an integer $$$N$$$, the second line contains an integer $$$K$$$ ($$$1 \le N \le 10^9$$$, $$$1 \le K \le N$$$).

Output

Оutput "Yes" if the claim with number $$$K$$$ will be signed, and "No" if it will be thrown away.

In the second line, output the step number during which this will happen.

Scoring

Solutions that runs correctly for $$$N \le 1000$$$ score 40 points.

Solutions that runs correctly for $$$N \le 5\cdot10^5$$$ score 60 points.

Examples
Input
4
3
Output
No
5
Input
5
3
Output
Yes
7
Note

In the first example in the problem, there are 4 claims in the pile: (1, 2, 3, 4). Claim 1 is signed, claim 2 is thrown away, and claim 3 is moved down to the bottom. After three steps, the pile will have claims (4, 3). Therefore, on the fifth step, claim 3 will be thrown away.

In the second example in the problem statement, the pile has claims (1, 2, 3, 4, 5). After three steps, the pile will look like (4, 5, 3). Over the next three steps, claim 4 will be signed, claim 5 will be thrown away, and claim 3 will be moved down the pile (which will contain nothing but claim 3). Therefore, after six steps, the pile will have the form (3). On the seventh step, claim 3 will be signed.