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 sys import stdin

def factor(a, k):
    factor=[]
    cur = 0
    while a != 0:
        if a % k == 0:
            a/=k
        elif a % k == 1:
            factor.append(cur)
            a=(a-1)/k
        else:
            return -1
        cur+=1
    return factor

T = int(stdin.readline())
for i in range(T):
    n, k = list(map(int, stdin.readline().split(" ")))
    A = list(map(int, stdin.readline().split(" ")))

    state=1
    dic={}
    for item in A:
        if item == 0:
            continue
        else:
            fact = factor(item, k)
            if fact == -1:
                print("NO")
                state=-1
                break
            for index in fact:
                if index not in dic:
                    dic[index] = 1
                else:
                    print("NO")
                    state = -1
                    break
            if state == -1:
                break
    if state == 1:
        print("YES")
