Alok-nath is man of equality. He needs your help to divide his “sanskars” evenly amongst all his followers. By doing this, Alok-nath can create equality amongst his followers and he'll be called a true “sanskari”.
Alok-nath has N sanskars, and K followers. Each sanskar is given a numerical value which shows its intensity.
Your task is to determine whether it is possible to allocate all the sanskars to followers in such a way that the sum of intensities of the sanskars allocated to each follower is equal. Note : A sanskar can be allocated to only one of the followers.

Input
The first line of the input contains an integer T, denoting the number of test cases. Then T test cases follow. The first line of each case contains two integers N and K, with N denoting the number of sanskars and K denoting the number of followers. In the next line are N space separated integers denoting the intensities of each sanskar.

Output
For each test case, output "yes" if it is possible to divide his sanskars equally amongst his followers; otherwise output "no" (without quotes).

Constraints

1 ≤ T ≤ 10
1 ≤ N ≤ 21
1 ≤ K ≤ 8
Example
Input:
2
5 3
1 2 4 5 6
5 3
1 2 4 5 7

Output:
yes
no

Explanation
In the first case, sanskars can be allocated as follows, each follower receiving a total intensity of 6: {1,5}, {2,4}, {6}.

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