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 JAVA):

Solution:
import java.util.*;
import java.lang.*;
import java.io.*;

//author: ankit_bit

public class Main {

    static FastReader fr = new FastReader();
    static StringBuilder sb = new StringBuilder();

    public static void main(String[] args) throws java.lang.Exception {

        int testcases = fr.nextInt();
        while (testcases-- > 0) {

            solve();

        }
        System.out.println(sb);
    }

    public static void solve() {
        long n= fr.nextLong();
        long a= fr.nextLong();
        long b= fr.nextLong();
        if(n==1)
            sb.append("Yes");
       else if(a==1){
           if(b==1 ||n%b==1)
               sb.append("Yes");
           else
               sb.append("No");
       }
       else{
          boolean found=false;
           long i=1;
          while(i<=n){
               if((n-i)%b==0){
                   found=true;
                   break;
               }
               i*=a;
           }
           if(found)
               sb.append("Yes");
           else sb.append("No");
       }
       sb.append("\n");
    }


    static long mult(long a, long b, long mod){
        long res=(a*b)%mod;
        if(res<0){
            res+=mod;
        }
        return res;
    }
    static long add(long a,long b,long mod){
        long res=(a+b)%mod;
        if(res<0){
            res+=mod;
        }
        return res;
    }

    static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    static long fact[] = new long[1001], M = 1000000007;

    static long ncr(int n, int r) {
        if (r > n) return 0;
        return fact[n] * power(fact[r], M - 2) % M * power(fact[n - r], M - 2) % M;
    }

    static long power(long a, long b) {
        long res = 1;
        while (b != 0) {
            if (b % 2 == 1) res = res * a % M;
            b >>= 1;
            a = a * a % M;
        }
        return res;
    }


    static void sort(long a[]) {
        ArrayList<Long> l = new ArrayList<>();
        for (int i = 0; i < a.length; i++) {
            l.add(a[i]);
        }
        Collections.sort(l);
        for (int i = 0; i < l.size(); i++)
            a[i] = l.get(i);
    }

}


class FastReader {
    BufferedReader br;
    StringTokenizer st;

    public FastReader() {
        br = new BufferedReader(new
                InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}