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 CPP):

Solution:
#include <bits/stdc++.h>
#define fastIO  std::ios::sync_with_stdio(false);cin.tie(NULL)
using namespace std;
#define int long long int
#define vi vector<int>
#define vvi vector<vector<int>>
#define pii pair<int,int>
#define ff first
#define ss second
#define mod 1000000007
#define MMOD  998244353
#define pb push_back
#define PI  3.1415926535897
using namespace std;
int gcd(int a, int b)
{
  if (b == 0)
    return a;
  return gcd(b, a % b);
 
}
 
 
signed main(void)
{
  int t = 1;
  fastIO;
  cin >> t;
  while (t--)
  {
    int a,b,i,j,n,flag=0,x;
    cin>>n>>a>>b;
    
    //n= a^x + b*y
    if(a==1)
    {
        if ((n - 1) % b == 0)
        flag = 1;
    }
    else{
    x=1;
      while (x <= n)
      {
        if ((n - x) % b == 0)
        {
          flag = 1;
          break;
        }
        x = x * a;
      }
    }
    if(flag)
    cout<<"YES\n";
    else cout<<"NO\n";
  }
}