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 os
import sys
from io import BytesIO, IOBase
import math

def main():
    pass

BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")


def binary(n):
    return (bin(n).replace("0b", ""))


def decimal(s):
    return (int(s, 2))


def pow2(n):
    p = 0
    while (n > 1):
        n //= 2
        p += 1
    return (p)


def primeFactors(n):
    l=[]
    while n % 2 == 0:
        l.append(2)
        n = n / 2
    for i in range(3, int(math.sqrt(n)) + 1, 2):
        while n % i == 0:
            l.append(i)
            n = n / i
    if n > 2:
        l.append(int(n))
    return (l)


def isPrime(n):
    if (n == 1):
        return (False)
    else:
        root = int(n ** 0.5)
        root += 1
        for i in range(2, root):
            if (n % i == 0):
                return (False)
        return (True)

def maxPrimeFactors(n):
    maxPrime = -1
    while n % 2 == 0:
        maxPrime = 2
        n >>= 1
    for i in range(3, int(math.sqrt(n)) + 1, 2):
        while n % i == 0:
            maxPrime = i
            n = n / i
    if n > 2:
        maxPrime = n
    return int(maxPrime)


def reVal(num):
    if (num >= 0 and num <= 9):
        return chr(num + ord('0'));
    else:
        return chr(num - 10 + ord('A'));



def strev(str):
    len = len(str);
    for i in range(int(len / 2)):
        temp = str[i];
        str[i] = str[len - i - 1];
        str[len - i - 1] = temp;

def fromDeci(res, base, inputNum):
    index = 0;

    while (inputNum > 0):
        res += reVal(inputNum % base);
        inputNum = int(inputNum / base);

    res = res[::-1];

    return res;
def norm(s,l):
    tba="0"*(l-len(s))
    return(tba+s)
#print(fromDeci("",3,2))
for xyz in range(0,int(input())):
    n,k=map(int,input().split())
    l=list(map(int,input().split()))
    le=[]
    for i in l:
        if(i!=0):
            le.append(i)
    l=le.copy()
    bm=[]
    for i in l:
        bm.append(fromDeci("",k,i))
    if(len(l)==0):
        print("YES")

    else:
        f=True
        ma=max(l)
        n=len(l)
        for i in range(0,n):
            bm[i]=norm(bm[i],int(math.log(ma,k))+2)
        #print(bm)
        for i in bm:
            if(f):
                for j in i:
                    if(j!="1" and j!="0"):
                        f=False
                        break
        if(f):
            cnt=[0]*(len(bm[0]))
            for i in bm:
                for j in range(0,len(i)):
                    cnt[j]+=int(i[j])
            #print(cnt)
            if(max(cnt)>1):
                print("NO")
            else:
                print("YES")
        else:
            print("NO")
