Suppose you are performing the following algorithm. There is an array v_1, v_2, ..., v_n filled with zeroes at start. The following operation is applied to the array several times — at i-th step (0-indexed) you can: 

  * either choose position pos (1 ≤ pos ≤ n) and increase v_{pos} by k^i; 
  * or not choose any position and skip this step. 



You can choose how the algorithm would behave on each step and when to stop it. The question is: can you make array v equal to the given array a (v_j = a_j for each j) after some step?

Input

The first line contains one integer T (1 ≤ T ≤ 1000) — the number of test cases. Next 2T lines contain test cases — two lines per test case.

The first line of each test case contains two integers n and k (1 ≤ n ≤ 30, 2 ≤ k ≤ 100) — the size of arrays v and a and value k used in the algorithm.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^{16}) — the array you'd like to achieve.

Output

For each test case print YES (case insensitive) if you can achieve the array a after some step or NO (case insensitive) otherwise.

Example

Input


5
4 100
0 0 0 0
1 2
1
3 4
1 4 1
3 2
0 1 3
3 9
0 59049 810


Output


YES
YES
NO
NO
YES

Note

In the first test case, you can stop the algorithm before the 0-th step, or don't choose any position several times and stop the algorithm.

In the second test case, you can add k^0 to v_1 and stop the algorithm.

In the third test case, you can't make two 1 in the array v.

In the fifth test case, you can skip 9^0 and 9^1, then add 9^2 and 9^3 to v_3, skip 9^4 and finally, add 9^5 to v_2.
import sys
from collections import defaultdict
#import math

def main():
    def reVal(num):
        if (num >= 0 and num <= 9):
            return chr(num + ord('0'))
        else:
            return chr(num - 10 + ord('A'))

    def fromDeci(res, base, inputNum):
        while (inputNum > 0):
            res += reVal(inputNum % base)
            inputNum = int(inputNum / base)
        res = res[::-1]
        return res

    def check(q):
        for i in q:
            if i!='1' and i!='0':
                return True
        return False

    def setans(ans,q):
        x=len(q)
        for i in range(x):
            if q[i]=='1':
                ans[x-i-1]+=1

    for _ in range(int(sys.stdin.readline())):
        n,k = map(int,sys.stdin.readline().split())
        l = [int(y) for y in sys.stdin.readline().split()]
        ans = defaultdict(int)
        flag = 0
        for i in l:
            if i!=0:
                res=""
                q = fromDeci(res,k,i)
                #print(q)
                if check(q):
                    flag = 1
                    break
                setans(ans,q)
        for i in ans:
            if ans[i]!=1:
                flag=1
                break
        if flag == 1:
            print('NO')
        else:
            print('YES')

if __name__ == "__main__":
    main()