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.io.*;
import java.util.*;
public class Main {
    public static void main(String[] args) throws IOException {
        SolveQue solveQue = new SolveQue();
        solveQue.ques();
    }
}

class SolveQue {
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner()
        {
            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;
        }
    }
    private static final FastScanner fs = new FastScanner();
    private static final Scanner sc = new Scanner(System.in);
    private static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private static final long MOD = (long) (1e9 + 7);
    private static PrintWriter out = new PrintWriter(System.out);
    private static BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out));
    private static final int iInf = Integer.MAX_VALUE - (int) (1e6);
    private static final long lInf = Long.MAX_VALUE - (long) (1e6);
    private static int[] phi;

    /** Optimal(Maximum,Minimum) Answers
     * 1. Binary search
     * 2. Prefix Suffix
     * 3. Greedy (sorting searching)
     * 4. DP
     **/
    void solve(int T) throws IOException {
        long n = fs.nextLong();
        long a = fs.nextLong();
        long b = fs.nextLong();
        if (a == 1) {
            if ((n-1)%b == 0) {
                System.out.println("YES");
            } else {
                System.out.println("NO");
            }
            return;
        }
        long x = 1;
        while (x <= n) {
            if (x%b == n%b) {
                System.out.println("YES");
                return;
            }
            x *= a;
        }
        System.out.println("NO");
    }
    void ques() throws IOException{
        int t = 1;
        t = fs.nextInt();
//        t = Integer.parseInt(br.readLine());
        int tt = 1;
        while (t-- > 0) {
            solve(tt);
            tt++;
        }
        System.gc();
    }
}