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 collections import Counter
from collections import defaultdict
import math
import random
import heapq as hq
from math import sqrt
import sys
from functools import reduce


def input():
    return sys.stdin.readline().strip()


def iinput():
    return int(input())


def tinput():
    return input().split()


def rinput():
    return map(int, tinput())


def rlinput():
    return list(rinput())


mod = int(1e9)+7


def factors(n):
    return set(reduce(list.__add__,
                      ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))


# ----------------------------------------------------


# 1
# 8 2 3
# 01110000
# 1 4
# 2 4
# 5 8
def solve(s, n, l, r, prefix, k):
    # print(prefix)
    ans = 0
    for i in range(l, r+1):
        for j in range(i, r+1):
            ones = prefix[j]-prefix[i-1]
            zeros = j-i-ones+1
            # print(i, j, ones, zeros)
            if prefix[j]-prefix[i-1] <= k and zeros <= k:
                ans += 1
    return ans

def highestPowerof(n,k): 
  
    res=0
    while n>=k:
        n=n//k
        res+=1
    return res

if __name__ == "__main__":
    for _ in range(iinput()):
        n,k=rinput()
        a=rlinput()
        d=defaultdict(int)
        flag=True
        for i in a:
            while i>0:
                temp=highestPowerof(i,k)
                # print(temp-int(tem
                i-=int(pow(k,temp))
                if i>=0:
                    if d[temp]==1:
                        flag=False
                        break
                    d[temp]+=1
                # print(temp)
            if flag==False:
                break            
        print('YES' if flag else "NO")