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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.StringTokenizer;
 
 
public class Hello1 {
	static long mod = (long) 1e8;
	static FastReader s = new FastReader();
	public static void func(double[] arr, int num, int digits, double[][] matrix, int val, int num_ones) {
		if(num_ones == 1){
			arr[num] = 1.0;
			return;
		}
		double final_prob = 0;
		for(int i = 0; i < digits; i++) {
			
			if(i != val && (1 << (i) & num) != 0 ) {
				
				double prob = 0;
				int new_num = ((1 << (i)) ^ num);
				for(int j = 0; j < digits; j++) {
					if(j != i && ((1 << j) & num) != 0) {
						prob = prob + matrix[j][i];
					}
				}
				
				prob = prob / (((num_ones) * (num_ones - 1)) / 2);
				//System.out.println(Integer.toBinaryString(new_num) + " " + i + " " + prob);
				if(arr[new_num] == -1) func(arr, new_num, digits, matrix, val, num_ones - 1);
				final_prob = final_prob + prob * arr[new_num];
			}
		}
		
		arr[num] = final_prob;
		
	}
	
	
	
	public static void main(String[] args)  throws IOException{
		
       // BufferedWriter output = new BufferedWriter(
        //        new OutputStreamWriter(System.out));
		long t = s.nextInt();	
		for(int i = 0; i < t; i++) {
			int n = s.nextInt();
			int a = s.nextInt();
			int b = s.nextInt();
			
			long num = 1; int ans = 0;
			if(a == 1) {
				if((n - 1) % b == 0) System.out.println("Yes");
				else System.out.println("No");
				continue;
			}
			while(num <= n) {
				if((n - num) % b == 0) {
					ans = 1;
					break;
				}
				num = num * a;
			}
			if(ans == 1) System.out.println("Yes");
			else System.out.println("No");
		}
			
			
	}
}
 
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();
    }
 
    public 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;
}}