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.BufferedReader;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;
//import java.util.*;
public class Solution {
    static class FastScanner {

        BufferedReader br;
        StringTokenizer st ;

        FastScanner(){
            br =  new BufferedReader(new InputStreamReader(System.in));
            st = new StringTokenizer("");
        }

        FastScanner(String file) {

            try {
                br =  new BufferedReader(new InputStreamReader(new FileInputStream(file)));
                st = new StringTokenizer("");
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                System.out.println("file not found");
                e.printStackTrace();
            }
            
        }
        

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

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

        long nextLong() {
            return Long.parseLong(next());
        }
        String readLine() throws IOException{
            return br.readLine();
        }
    }

    

    public static void main(String[] args) throws Exception {
        FastScanner s = new FastScanner();

        int t = s.nextInt();

        for(int tc=0;tc<t;tc++){
            
            long  n = s.nextLong();
            long  a = s.nextLong();
            long  b = s.nextLong();

            boolean av = false;

            // long log = (long)(Math.log(n)/Math.log(a));

            // long power = (long)Math.ceil(Math.pow(a,log));

            if(a == 1){
                if(((n-1l) % b) == 0l){
                    System.out.println("Yes");
                }else{
                    System.out.println("No");
                }
                continue;
            }

            //if(power == n){av=true;}
            //else if(n % b == 0l){av=true;}
            
                for(long i=0;((long)Math.pow(a,i))<=n;i++){
                    if(((n - ((long)Math.pow(a,i))) % b) == 0l){
                        av = true;break;
                    }
                }
            

            System.out.println((av?"Yes":"No"));

        }
    

    }

    static boolean isPower(long n,long a){
        
        long log = (long)(Math.log(n)/Math.log(a));

        long power = (long)Math.pow(a,log);

        if(power == n){return true;}

        return false;
    }

 
    private static int mergeAndCount(int[] arr, int l,int m, int r)
    {
 
        // Left subarray
        int[] left = Arrays.copyOfRange(arr, l, m + 1);
 
        // Right subarray
        int[] right = Arrays.copyOfRange(arr, m + 1, r + 1);
 
        int i = 0, j = 0, k = l, swaps = 0;
 
        while (i < left.length && j < right.length) {
            if (left[i] <= right[j])
                arr[k++] = left[i++];
            else {
                arr[k++] = right[j++];
                swaps += (m + 1) - (l + i);
            }
        }
        while (i < left.length)
            arr[k++] = left[i++];
        while (j < right.length)
            arr[k++] = right[j++];
        return swaps;
    }
 
    // Merge sort function
    private static int mergeSortAndCount(int[] arr, int l,int r)
    {
 
        // Keeps track of the inversion count at a
        // particular node of the recursion tree
        int count = 0;
 
        if (l < r) {
            int m = (l + r) / 2;
 
            // Total inversion count = left subarray count
            // + right subarray count + merge count
 
            // Left subarray count
            count += mergeSortAndCount(arr, l, m);
 
            // Right subarray count
            count += mergeSortAndCount(arr, m + 1, r);
 
            // Merge count
            count += mergeAndCount(arr, l, m, r);
        }
 
        return count;
    }
 
    
   
}