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.
import sys
import math
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__

#print(math.log(9999999999999999,100))

def getit(num,base):
    res=[]
    while True:
        if num==0:
            return res
        else:
            
            lognum=int(math.log(num,base))
            revnorm=base**lognum
            revnormp1=base**(lognum+1)
            revnormm1=base**(lognum-1)
            #print(res,lognum,revnorm,num,revnormp1)

            if lognum==0 and revnorm!=num  or revnormp1!=revnormp1:
                #print('con1')
                return False  
            elif revnorm==num:
                #print('con2')
                num=0
                res.append(lognum)
            elif revnormp1==num:
                #print('con3')
                num=0
                res.append(lognum+1)
            else:
                #print('con4')
                if num<revnorm:
                    num-=revnormm1
                    if lognum-1 in res:
                        return False 
                    res.append(lognum-1)                    
                elif num<revnormp1:
                    num-=revnorm
                    if lognum in res:
                        return False 
                    res.append(lognum)
                else:
                    num-=revnormp1
                    if lognum+1 in res:
                        return False 
                    res.append(lognum+1)
                       
            
def gift():
    for _ in range(t):
        n,k = list(map(int,input().split()))
        array=list(map(int,input().split()))
        gotarr=[]
        found=True
        for ele in array:
            logitnum=getit(ele,k)
            #print(ele,k,logitnum)
            if not found:
                break
            else:
                if ele:
                    if logitnum:
                        for nums in logitnum:
                            if nums not in gotarr:
                                gotarr.append(nums)
                            else:
                                found=False
                                break
                                
                    else:
                        found=False
        #print(gotarr)
        if found:
            yield 'YES'
        else:
            yield 'NO'


if __name__ == '__main__':
    t= int(input())
    ans = gift()
    print(*ans,sep='\n')
            
