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

input = sys.stdin.readline

def conv_strLs2intLs(line):
    a_list = line.split()
    map_object = map(int, a_list)
    list_of_integers = list(map_object)
    return list_of_integers  

def nu_bgst_power(nu,base):
    pow=math.log(nu,base)
    ctmp=math.ceil(pow)
    ftmp=math.floor(pow)
    pow=ctmp if ctmp-pow<0.0000000000001 else ftmp
    nu2=int(math.pow(base,pow))
    if nu2-nu>0:
        return pow-1
    return pow

count =int(input())
for line in range(count): 
    content1=input().split()
    n=int(content1[0])
    k=int(content1[1])
    array=input().split()
    result="YES"
    usedIndexes=set()
    for nu in array:
        newnu=int(nu)
        while newnu!=0:
            index=nu_bgst_power(newnu,k)
            if index in usedIndexes:
                result="NO"
                break
            usedIndexes.add(index)
            newnu-=k**index
        if result=="NO":
            break

    print(result)
