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.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringTokenizer;

public class n729B {

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int t = sc.ni();
        while (t -- > 0) {
            int n = sc.ni();
            int a = sc.ni();
            int b = sc.ni();
            if (a == 1) {
                if ((n - 1) % b == 0)
                    System.out.println("Yes");
                else
                    System.out.println("No");
            } else {
                int r = judge(n, a, b);
                if (r == 1)
                    System.out.println("Yes");
                else
                    System.out.println("No");
            }
        }
    }

    static int judge(int n, int a, int b) {
        int k = (int)(Math.log(n) / Math.log(a));
//        System.out.println(k);
        for (int i = 0; i <= k + 5; i++) {
            int t = n - (int)Math.pow(a, i);
            if (t >= 0 && t % b == 0) {
//                System.out.println("k : " + i);
                return 1;
            }
        }
        return 0;
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in), 32768);
            st = null;
        }

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

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

        int[][] graph(int N, int[][] edges) {
            int[][] graph = new int[N][];
            int[] sz = new int[N];
            for (int[] e: edges) {
                sz[e[0]] += 1;
                sz[e[1]] += 1;
            }
            for (int i = 0; i < N; i++) {
                graph[i] = new int[sz[i]];
            }
            int[] cur = new int[N];
            for (int[] e: edges) {
                graph[e[0]][cur[e[0]]] = e[1];
                graph[e[1]][cur[e[1]]] = e[0];
                cur[e[0]] += 1;
                cur[e[1]] += 1;
            }
            return graph;
        }

        int[] intArray(int N, int mod) {
            int[] ret = new int[N];
            for (int i = 0; i < N; i++)
                ret[i] = ni()+mod;
            return ret;
        }

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

        long[] longArray(int N, long mod) {
            long[] ret = new long[N];
            for (int i = 0; i < N; i++)
                ret[i] = nl()+mod;
            return ret;
        }

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

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