B. All Pairs Segments
time limit per test
1.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Shirobon - FOX
⠀

You are given $$$n$$$ points on the $$$x$$$ axis, at increasing positive integer coordinates $$$x_1 < x_2 < \ldots < x_n$$$.

For each pair $$$(i, j)$$$ with $$$1 \leq i < j \leq n$$$, you draw the segment $$$[x_i, x_j]$$$. The segments are closed, i.e., a segment $$$[a, b]$$$ contains the points $$$a, a+1, \ldots, b$$$.

You are given $$$q$$$ queries. In the $$$i$$$-th query, you are given a positive integer $$$k_i$$$, and you have to determine how many points with integer coordinates are contained in exactly $$$k_i$$$ segments.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$, $$$q$$$ ($$$2 \le n \le 10^5$$$, $$$1 \le q \le 10^5$$$) — the number of points and the number of queries.

The second line of each test case contains $$$n$$$ integers $$$x_1, x_2, \ldots, x_n$$$ ($$$1 \leq x_1 < x_2 < \ldots < x_n \leq 10^9$$$) — the coordinates of the $$$n$$$ points.

The third line of each test case contains $$$q$$$ integers $$$k_1, k_2, \ldots, k_q$$$ ($$$1 \leq k_i \leq 10^{18}$$$) — the parameters of the $$$q$$$ queries.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$, and the sum of $$$q$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, output a single line with $$$q$$$ integers: the $$$i$$$-th integer is the answer to the $$$i$$$-th query.

Example
Input
3
2 2
101 200
2 1
6 15
1 2 3 5 6 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
5 8
254618033 265675151 461318786 557391198 848083778
6 9 15 10 6 9 4 4294967300
Output
0 100 
0 0 0 0 2 0 0 0 3 0 2 0 0 0 0 
291716045 0 0 0 291716045 0 301749698 0
Note

In the first example, you only draw the segment $$$[101, 200]$$$. No point is contained in exactly $$$2$$$ segments, and the $$$100$$$ points $$$101, 102, \ldots, 200$$$ are contained in exactly $$$1$$$ segment.

In the second example, you draw $$$15$$$ segments: $$$[1, 2], [1, 3], [1, 5], [1, 6], [1, 7], [2, 3], [2, 5], [2, 6], [2, 7], [3, 5], [3, 6], [3, 7], [5, 6], [5, 7], [6, 7]$$$. Points $$$1, 7$$$ are contained in exactly $$$5$$$ segments; points $$$2, 4, 6$$$ are contained in exactly $$$9$$$ segments; points $$$3, 5$$$ are contained in exactly $$$11$$$ segments.