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.math.BigInteger;

import java.io.*;

public class Main implements Runnable {

    public static void main(String[] args) {
        new Thread(null, new Main(), "whatever", 1 << 26).start();
    }


    private FastScanner sc;
    private PrintWriter pw;

    public void run() {
        try {
            // pw = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
            // sc = new FastScanner(new BufferedReader(new FileReader("input.txt")));
            pw = new PrintWriter(System.out);
            sc = new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
        } catch (Exception e) {
            throw new RuntimeException();
        }
        int t = sc.nextInt();
        // int t = 1;
        while (t-- > 0) {
            // sc.nextLine();
            solve();
        }
        pw.close();
    }

    public long mod = 1_000_000_007;

    public void solve() {
        int n = sc.nextInt();
        int a = sc.nextInt();
        int b = sc.nextInt();

        if (n == 1) {
            pw.println("YES");
            return;
        }

        if (a == 1) {
            if ((n - 1) % b == 0) {
                pw.println("YES");
                return;
            } else {
                pw.println("NO");
                return;
            }
        }
        long temp;
        for (long x = 1; x <= n; x *= a) {
            temp = n - x;
            temp %= b;
            if (temp == 0) {
                pw.println("YES");
                return;
            }
        }
        pw.println("NO");
    }

    class FastScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public FastScanner(BufferedReader bf) {
            reader = bf;
            tokenizer = null;
        }

        public String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

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

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

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

        public float nextFloat() {
            return Float.parseFloat(next());
        }

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public String[] nextStringArray(int n) {
            String[] a = new String[n];
            for (int i = 0; i < n; i++) {
                a[i] = next();
            }
            return a;
        }

        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }

    }

    public long fastPow(long x, long y, long mod) {
        if (y == 0) return 1;
        if (y == 1) return x % mod;

        long temp = fastPow(x, y / 2, mod);
        long ans = (temp * temp) % mod;

        return (y % 2 == 1) ? (ans * (x % mod)) % mod : ans;
    }

// public long fastPow(long x, long y) {
//     if (y == 0) return 1;
//     if (y == 1) return x;

//     long temp = fastPow(x, y / 2);
//     long ans = (temp * temp);

//     return (y % 2 == 1) ? (ans * x) : ans;
// }

}