Problem: There is an infinite set generated as follows:

  * 1 is in this set. 
  * If x is in this set, x ⋅ a and x+b both are in this set. 



For example, when a=3 and b=6, the five smallest elements of the set are:

  * 1, 
  * 3 (1 is in this set, so 1⋅ a=3 is in this set), 
  * 7 (1 is in this set, so 1+b=7 is in this set), 
  * 9 (3 is in this set, so 3⋅ a=9 is in this set), 
  * 13 (7 is in this set, so 7+b=13 is in this set). 



Given positive integers a, b, n, determine if n is in this set.

Input

The input consists of multiple test cases. The first line contains an integer t (1≤ t≤ 10^5) — the number of test cases. The description of the test cases follows.

The only line describing each test case contains three integers n, a, b (1≤ n,a,b≤ 10^9) separated by a single space.

Output

For each test case, print "Yes" if n is in this set, and "No" otherwise. You can print each letter in any case.

Example

Input


5
24 3 5
10 3 6
2345 1 4
19260817 394 485
19260817 233 264


Output


Yes
No
Yes
No
Yes

Note

In the first test case, 24 is generated as follows:

  * 1 is in this set, so 3 and 6 are in this set; 
  * 3 is in this set, so 9 and 8 are in this set; 
  * 8 is in this set, so 24 and 13 are in this set. 



Thus we can see 24 is in this set.

The five smallest elements of the set in the second test case is described in statements. We can see that 10 isn't among them.

Solution (in PYTHON3):

Solution:
'''
    Auther: ghoshashis545 Ashis Ghosh
    College: Jalpaiguri Govt Enggineering College

'''
from os import path
from io import BytesIO, IOBase
import sys
from heapq import heappush,heappop
from functools import cmp_to_key as ctk
from collections import deque,Counter,defaultdict as dd 
from bisect import bisect,bisect_left,bisect_right,insort,insort_left,insort_right
from itertools import permutations
from datetime import datetime
from math import ceil,sqrt,log,gcd
def ii():return int(input())
def si():return input().rstrip()
def mi():return map(int,input().split())
def li():return list(mi())
abc='abcdefghijklmnopqrstuvwxyz'
mod=1000000007
#mod=998244353
inf = float("inf")
vow=['a','e','i','o','u']
dx,dy=[-1,1,0,0],[0,0,1,-1]

def bo(i):
    return ord(i)-ord('0')

file = 1
def ceil(a,b):
    return (a+b-1)//b




def solve():

    
    for _ in range(1,ii()+1):
        n,a,b = mi()
        x = [1,a]
        for i in range(30):
            x.append(x[-1]*a)
            if x[-1]>1e9:
                break
        n1 = len(x)
        ok = True
        for i in range(n1):
            if n%x[i]==0:
                n2 = n//x[i]
                for j in range(n1): 
                    if n2 >= x[j] and (n2-x[j])%b==0:
                        print("YES")
                        ok = False
                        break
            if ok==False:
                break
        if ok:
            print("NO")







            





    
        








        
if __name__ =="__main__":

    if(file):
    
       if path.exists('input.txt'):
           sys.stdin=open('input.txt', 'r')
           sys.stdout=open('output.txt','w')
       else:
           input=sys.stdin.readline
    solve()