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
from collections import defaultdict
#####################################################################
def iinput(): return int(stdin.readline())
def sinput(): return input()
def minput(): return map(int, stdin.readline().split())
def linput(): return list(map(int, stdin.readline().split()))
#####################################################################

def power(n, k):
    i = 0
    while n%k==0:
        n//=k
        i+=1
    return i

t = iinput()
while t:
    t-=1
    n, k =minput()
    a = linput()
    v = [0]*n
    ans = 'YES'
    if a == v:
        print(ans)
    else:
        a.sort()
        c = defaultdict(int)
        for j in range(n):
            if a[j]==1:
                c[0]+=1
                if c[0]>1:
                    ans = 'NO'
                    break
            elif a[j]>1:
                while True:
                    p = power(a[j], k)
                    a[j] = a[j] - k**p
                    if 1<a[j]<k:
                        ans = 'NO'
                        break
                    c[p]+=1
                    if c[p]>1:
                        ans = 'NO'
                        break
                    if a[j]==0:break
                if ans == 'NO':break
        print(ans)