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.
z=input
mod = 10**9 + 7
from collections import *
from queue import *
from sys import *
from collections import *
from math import *
from heapq import *
from itertools import *
from bisect import *
from collections import Counter as cc
from math import factorial as f
def lcd(xnum1,xnum2):
    return (xnum1*xnum2//gcd(xnum1,xnum2))

################################################################################

"""

n=int(z())

for _ in range(int(z())):

x=int(z())

l=list(map(int,z().split()))

n=int(z())

l=sorted(list(map(int,z().split())))[::-1]

a,b=map(int,z().split())

l=set(map(int,z().split()))

led=(6,2,5,5,4,5,6,3,7,6)

vowel={'a':0,'e':0,'i':0,'o':0,'u':0}

color-4=["G", "GB", "YGB", "YGBI", "OYGBI" ,"OYGBIV",'ROYGBIV' ]

"""

###########################---START-CODING---###############################################
"""
3
4
1 7 6 5
5
1 2 3 4 5
2
0 -4
"""


for _ in range(int(z())):
    n,k=map(int,z().split())
    l=list(map(int,z().split()))
    d=[0]*100
    for i in range(n):
        x=l[i]
        c=0
        while x>0:
            d[c]+=x%k
            c+=1
            x=x//k
     
    if max(d)>1:
        print('No')
    else:
        print('yEs')
            
   
    
    
        
        



        
        
