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.
def bin(a, b):
    res = 1
    while b > 0:
        if b & 1:
            res = res * a
        a *= a
        b >>= 1
    return res


I = lambda: list(map(int, input().split()))
for _ in range(int(input())):
    n, k = I()
    l = I()
    maxx = 1e16
    s = 1
    while bin(k, s) <= 1e16:
        s += 1
    s -= 1
    max_val = bin(k, s)
    flag = False
    for i in range(s, -1, -1):
        max_val = bin(k, i)
        count = 0
        for j in range(len(l)):
            if l[j] >= max_val:
                l[j] -= max_val
                count += 1
            if count > 1:
                flag = True
                print('NO')
                break
        if flag:
            break
    if not flag:
        flag2 = False
        for e in l:
            if e != 0:
                print('NO')
                flag2 = True
                break
        if not flag2:
            print('YES')

