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:
# Problem: B. Plus and Multiply
# Contest: Codeforces - Codeforces Round #729 (Div. 2)
# URL: https://codeforces.com/contest/1542/problem/B
# Memory Limit: 512 MB
# Time Limit: 3000 ms
# 
# Powered by CP Editor (https://cpeditor.org)

# ____           ____   ___         # skeon19
#|      | /     |      |   | |\   | # 
#|____  |/      |___   |   | | \  | # EON_KID
#     |	|\      |      |   | |  \ | #
# ____|	| \ ___ |____  |___| |   \| # Soul_Silver

from collections import defaultdict
import sys,io,os
INP=sys.stdin.readline
inp=lambda:[*map(int,INP().encode().split())]
sinp=lambda:[*map(str,INP().split())]
out=sys.stdout.write
#from functools import reduce
#from bisect import bisect_right,bisect_left
#from sortedcontainers import SortedList, SortedSet, SortedDict
#import sympy #Prime number library
#import heapq

def main():
    for _ in range(inp()[0]):
        n,a,b=inp()
        if b==1:
        	print("Yes")
        	continue
        if a==1:
        	if n%b!=1:
        		print("No")
        	else:
        		print("Yes")
        	continue
        
        check=0
        fist=1
        while fist<=n:
        	if not (n-fist)%b:
        		check=1
        	fist*=a
        if not check:
        	print("No")
        else:
        	print("Yes")
        
        
        
        
###############################################################       
def SumOfExpOfFactors(a):
	fac = 0
	lis=SortedList()
	if not a&1: 
		lis.add(2)
	while not a&1:
		a >>= 1
		fac += 1
	for i in range(3,int(a**0.5)+1,2):
		if not a%i:
			lis.add(i)
		while not a%i:
			a //= i
			fac += 1
	if a != 1:
		lis.add(a)
		fac += 1
	return fac,lis
###############################################################
div=[0]*(1000001)
def NumOfDivisors(n): #O(nlog(n))
	for i in range(1,n+1):
		for j in range(i,n+1,i):
			div[j]+=1
###############################################################
def primes1(n): #return a list having prime numbers from 2 to n
    """ Returns  a list of primes < n """
    sieve = [True] * (n//2)
    for i in range(3,int(n**0.5)+1,2):
        if sieve[i//2]:
            sieve[i*i//2::i] = [False] * ((n-i*i-1)//(2*i)+1)
    return [2] + [2*i+1 for i in range(1,n//2) if sieve[i]]
##############################################################    
def GCD(a,b):
    if(b==0):
        return a
    else:
        return GCD(b,a%b)
##############################################################
#
#     1
#   /   \
#  2     3
# /\   / \ \ \
#4  5  6 7 8 9
#      \
#      10

class Graph:
    def __init__(self):
        self.Graph = defaultdict(list)
        
    def addEdge(self, u, v):
        self.Graph[u].append(v)
        self.Graph[v].append(u)
    #DFS Graph / tree    
    def DFSUtil(self, v, visited):
        visited.add(v)
        #print(v, end=' ')
        for neighbour in self.Graph[v]:
            if neighbour not in visited: #not needed if its a tree
                self.DFSUtil(neighbour, visited)
    def DFS(self, v):
 
        visited = set() #not needed if its a tree
        self.DFSUtil(v, visited) #Visited not needed if its a tree
    #BFS Graph / tree
    def BFS(self, s):
        # Mark all the vertices as not visited
        
        visited = set()
        # Create a queue for BFS
        queue = []
        queue.append(s)
        visited.add(s)
        while queue:
            s = queue.pop(0)
            #print (s, end = " ")
            for i in self.Graph[s]:
                if i not in visited:
                    queue.append(i)
                    visited.add(i)
'''
g = Graph()
g.addEdge(1, 2)
g.addEdge(1, 3)
g.addEdge(2, 4)
g.addEdge(2, 5)
g.addEdge(3, 6)
g.addEdge(3, 7)
g.addEdge(3, 8)
g.addEdge(3, 9)
g.addEdge(6,10)
g.DFS(1)  
g.BFS(1)  '''   
##############################################################
class SortedList:
    def __init__(self, iterable=[], _load=200):
        """Initialize sorted list instance."""
        values = sorted(iterable)
        self._len = _len = len(values)
        self._load = _load
        self._lists = _lists = [values[i:i + _load] for i in range(0, _len, _load)]
        self._list_lens = [len(_list) for _list in _lists]
        self._mins = [_list[0] for _list in _lists]
        self._fen_tree = []
        self._rebuild = True

    def _fen_build(self):
        """Build a fenwick tree instance."""
        self._fen_tree[:] = self._list_lens
        _fen_tree = self._fen_tree
        for i in range(len(_fen_tree)):
            if i | i + 1 < len(_fen_tree):
                _fen_tree[i | i + 1] += _fen_tree[i]
        self._rebuild = False

    def _fen_update(self, index, value):
        """Update `fen_tree[index] += value`."""
        if not self._rebuild:
            _fen_tree = self._fen_tree
            while index < len(_fen_tree):
                _fen_tree[index] += value
                index |= index + 1

    def _fen_query(self, end):
        """Return `sum(_fen_tree[:end])`."""
        if self._rebuild:
            self._fen_build()

        _fen_tree = self._fen_tree
        x = 0
        while end:
            x += _fen_tree[end - 1]
            end &= end - 1
        return x

    def _fen_findkth(self, k):
        """Return a pair of (the largest `idx` such that `sum(_fen_tree[:idx]) <= k`, `k - sum(_fen_tree[:idx])`)."""
        _list_lens = self._list_lens
        if k < _list_lens[0]:
            return 0, k
        if k >= self._len - _list_lens[-1]:
            return len(_list_lens) - 1, k + _list_lens[-1] - self._len
        if self._rebuild:
            self._fen_build()

        _fen_tree = self._fen_tree
        idx = -1
        for d in reversed(range(len(_fen_tree).bit_length())):
            right_idx = idx + (1 << d)
            if right_idx < len(_fen_tree) and k >= _fen_tree[right_idx]:
                idx = right_idx
                k -= _fen_tree[idx]
        return idx + 1, k

    def _delete(self, pos, idx):
        """Delete value at the given `(pos, idx)`."""
        _lists = self._lists
        _mins = self._mins
        _list_lens = self._list_lens

        self._len -= 1
        self._fen_update(pos, -1)
        del _lists[pos][idx]
        _list_lens[pos] -= 1

        if _list_lens[pos]:
            _mins[pos] = _lists[pos][0]
        else:
            del _lists[pos]
            del _list_lens[pos]
            del _mins[pos]
            self._rebuild = True

    def _loc_left(self, value):
        """Return an index pair that corresponds to the first position of `value` in the sorted list."""
        if not self._len:
            return 0, 0

        _lists = self._lists
        _mins = self._mins

        lo, pos = -1, len(_lists) - 1
        while lo + 1 < pos:
            mi = (lo + pos) >> 1
            if value <= _mins[mi]:
                pos = mi
            else:
                lo = mi

        if pos and value <= _lists[pos - 1][-1]:
            pos -= 1

        _list = _lists[pos]
        lo, idx = -1, len(_list)
        while lo + 1 < idx:
            mi = (lo + idx) >> 1
            if value <= _list[mi]:
                idx = mi
            else:
                lo = mi

        return pos, idx

    def _loc_right(self, value):
        """Return an index pair that corresponds to the last position of `value` in the sorted list."""
        if not self._len:
            return 0, 0

        _lists = self._lists
        _mins = self._mins

        pos, hi = 0, len(_lists)
        while pos + 1 < hi:
            mi = (pos + hi) >> 1
            if value < _mins[mi]:
                hi = mi
            else:
                pos = mi

        _list = _lists[pos]
        lo, idx = -1, len(_list)
        while lo + 1 < idx:
            mi = (lo + idx) >> 1
            if value < _list[mi]:
                idx = mi
            else:
                lo = mi

        return pos, idx

    def add(self, value):
        """Add `value` to sorted list."""
        _load = self._load
        _lists = self._lists
        _mins = self._mins
        _list_lens = self._list_lens

        self._len += 1
        if _lists:
            pos, idx = self._loc_right(value)
            self._fen_update(pos, 1)
            _list = _lists[pos]
            _list.insert(idx, value)
            _list_lens[pos] += 1
            _mins[pos] = _list[0]
            if _load + _load < len(_list):
                _lists.insert(pos + 1, _list[_load:])
                _list_lens.insert(pos + 1, len(_list) - _load)
                _mins.insert(pos + 1, _list[_load])
                _list_lens[pos] = _load
                del _list[_load:]
                self._rebuild = True
        else:
            _lists.append([value])
            _mins.append(value)
            _list_lens.append(1)
            self._rebuild = True

    def discard(self, value):
        """Remove `value` from sorted list if it is a member."""
        _lists = self._lists
        if _lists:
            pos, idx = self._loc_right(value)
            if idx and _lists[pos][idx - 1] == value:
                self._delete(pos, idx - 1)

    def remove(self, value):
        """Remove `value` from sorted list; `value` must be a member."""
        _len = self._len
        self.discard(value)
        if _len == self._len:
            raise ValueError('{0!r} not in list'.format(value))

    def pop(self, index=-1):
        """Remove and return value at `index` in sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        value = self._lists[pos][idx]
        self._delete(pos, idx)
        return value

    def bisect_left(self, value):
        """Return the first index to insert `value` in the sorted list."""
        pos, idx = self._loc_left(value)
        return self._fen_query(pos) + idx

    def bisect_right(self, value):
        """Return the last index to insert `value` in the sorted list."""
        pos, idx = self._loc_right(value)
        return self._fen_query(pos) + idx

    def count(self, value):
        """Return number of occurrences of `value` in the sorted list."""
        return self.bisect_right(value) - self.bisect_left(value)

    def __len__(self):
        """Return the size of the sorted list."""
        return self._len

    def __getitem__(self, index):
        """Lookup value at `index` in sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        return self._lists[pos][idx]

    def __delitem__(self, index):
        """Remove value at `index` from sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        self._delete(pos, idx)

    def __contains__(self, value):
        """Return true if `value` is an element of the sorted list."""
        _lists = self._lists
        if _lists:
            pos, idx = self._loc_left(value)
            return idx < len(_lists[pos]) and _lists[pos][idx] == value
        return False

    def __iter__(self):
        """Return an iterator over the sorted list."""
        return (value for _list in self._lists for value in _list)

    def __reversed__(self):
        """Return a reverse iterator over the sorted list."""
        return (value for _list in reversed(self._lists) for value in reversed(_list))

    def __repr__(self):
        """Return string representation of sorted list."""
        return 'SortedList({0})'.format(list(self))
    # https://github.com/cheran-senthil/PyRival/blob/master/pyrival/data_structures/SortedList.py
###################################################################################################

if __name__ == '__main__':
    main()