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, stdout
from collections import Counter, defaultdict
from itertools import permutations, combinations
from fractions import gcd
import heapq
raw_input = stdin.readline
pr = stdout.write
mod=10**9+7

def ni():
    return int(raw_input())


def li():
    return list(map(int,raw_input().split()))


def pn(n):
    stdout.write(str(n)+'\n')


def pa(arr):
    pr(' '.join(map(str,arr))+'\n')

# fast read function for total integer input

def inp():
    # this function returns whole input of
    # space/line seperated integers 
    # Use Ctrl+D to flush stdin.
    return tuple(map(int,stdin.read().split()))
    
range = xrange # not for python 3.0+

# main code

for t in range(ni()):
    n,k=li()
    l=li()
    p=1
    pw=0
    mx=max(l)
    while (p*k)<=mx:
        p*=k
        pw+=1
    q=[]
    for i in l:
        heapq.heappush(q,-i)
    while q and pw>=0:
        x=-heapq.heappop(q)
        #print p,x,q
        if p>x:
            heapq.heappush(q,-x)
            p/=k
            pw-=1
            continue
        x-=p
        p/=k
        pw-=1
        if x:
            heapq.heappush(q,-x)
    f=0
    for i in q:
        if i:
            f=1
            break
    if f:
        pr('NO\n')
    else:
        pr('YES\n')
    
    
        
        
