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:
import os
import sys
from io import BytesIO, IOBase

#<fast I/O>
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)
#</fast I/O>

#<I/O>
def scanf(datatype = str):
    return datatype(sys.stdin.readline().rstrip())

def printf(answer = ''):
    return sys.stdout.write(str(answer) + "\n")

def prints(answer):
    return sys.stdout.write(str(answer) + " ")

def map_input(datatype = str):
    return map(datatype, sys.stdin.readline().split())

def list_input(datatype = str):
    return list(map(datatype, sys.stdin.readline().split()))

def testcase(number: int, solve_function):
    for _ in range(number):
        printf(solve_function())
        # solve_function()
#</I/O>


#<solution>
# sys.setrecursionlimit(int(1e8))
# def rec(Set, n1, n, a, b):
#     if(n1 == n):
#         return True
#     if(n1 > n):
#         return
#     num1 = n1 * a
#     flag1 = False
#     flag2 = False
#     if(num1 not in Set):
#         Set.add(num1)
#         flag1 = rec(Set, num1, n, a, b)
    
#     if flag1:
#         return flag1

#     num2 = n1 + b
#     if(num2 not in Set):
#         Set.add(num2)
#         flag2 = rec(Set, num2, n, a, b)

#     return flag2

# def solve():
#     n, a, b = map_input(int)
#     Set = set()
#     Set.add(1)
#     ans = rec(Set, 1, n, a, b)
#     return 'Yes' if ans else 'No'

def solve():
    n, a, b = map_input(int)
    if(a == 1):
        if (n - 1) % b == 0:
            return 'Yes'
        return 'No'
    
    term = 1
    while(term <= n):
        if (n - term) % b == 0:
            return 'Yes'
        term *= a
    return 'No'
    
    



# solve()
t = scanf(int)
testcase(t,solve)
#</solution>