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}.
def possible(A, e, n):
    def rec(i, r):
        if r == 0:
            return True
        if i == n:
            return False
        if A[i] > 0 and r >= A[i]:
            p = rec(i + 1, r - A[i])
            if p:
                A[i] = 0
                return True
        p = rec(i + 1, r)
        if p:
            return True
        return False
    for i in xrange(k):
        if not rec(0, e):
            break
    else:
        return True
    return False
T = int(raw_input())
while T > 0:
    n, k = map(int, raw_input().split())
    a = map(int, raw_input().split())
    total = sum(a)
    if n < k:
        print "no"
    elif total % k == 0:
        if possible(a, sum(a)/k, n):
            print "yes"
        else:
            print "no"
    else:
        print "no"
    T -= 1