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 bisect

def powSum(num,k,arr):
	if num == 0:
		return
	if num<0:
		return 
	i = 0
	while(pow(k,i)<=num):
		i+=1
	i-=1
	num -= pow(k,i)
	arr.append(i)
	powSum(num,k,arr)


arr = []

t  = int(input())

for _ in range(t):
	superSet = set()
	n,k = map(int,input().split(' '))
	a  = list(map(int,input().split(' ')))
	flag = True
	#print(f"tc : {a}")
	for num in a:
		arr = []
		powSum(num,k,arr)
		#print(f'powerset for {num} is {arr}')
		sa = set(arr)
		if len(sa)!=len(arr):
			print("NO")
			flag = False
			break
		else:
			#print(f'superSet is {superSet}')
			inter = superSet.intersection(sa)
			if len(inter)>0:
				print("NO")
				flag = False
				break
			else:
				#print('This ran')
				for e in sa:
					superSet.add(e)
	if flag:
		print("YES")





