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.
from bisect import bisect_left as lower_bound, bisect_right as upper_bound
from sys import stdin, stdout
from collections import defaultdict
from math import log10


def solve(num, k, seen):
    max_power = int(log10(num)/log10(k)) + 3

    for i in range(max_power, -1, -1):
        if k**i <= num:
            if seen[i]: return False

            num -= k**i
            seen[i] = True

    return (num == 0)

def main():
    t = int(input())

    for _ in range(t):
        n, k = list(map(int, input().strip().split()))
        arr = list(map(int, input().strip().split()))
        
        a = []
        for num in arr:
            if num: a.append(num)

        a.sort()
        seen = [False for _ in range(64)]

        f = False

        for num in a:
            if not solve(num, k, seen):
                f = True
                break

        if f: print("NO")
        else: print("YES")

if __name__ == "__main__": main()
