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 PlusandMultiply {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		// System.in and System.out are input and output streams, respectively.
		InputStream inputStream = System.in;

		InputReader in = new InputReader(inputStream);
		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
		int t = in.nextInt();
		while (t-- != 0) {
			int n = in.nextInt();
			int a = in.nextInt();
			int b = in.nextInt();

			if (b == 1) {
				out.write("Yes\n");
			} else if (a == 1) {
				if ((n - 1) % b == 0) {
					out.write("Yes\n");
				} else {
					out.write("No\n");
				}
			} else {

				long num = 1;
				boolean flag = false;
				while (num <= n) {
					if ((n - num) % b == 0) {
						flag = true;
						break;
					}
					num *= a;
				}
				if(flag) out.write("Yes\n");
				else out.write("No\n");
			}

		}
		out.close();
	}

	public static boolean isThere(int num, int n, HashMap<Integer, Boolean> strg, int a, int b) {
		if (num == n)
			return true;
		else if (num > n)
			return false;

		if (strg.containsKey(num))
			return strg.get(num);
		boolean fc = false;
		if (a != 1)
			fc = isThere(num * a, n, strg, a, b);
		if (fc) {
			strg.put(num, fc);
			return true;
		}
		boolean sc = isThere(num + b, n, strg, a, b);
		strg.put(num, sc);
		return sc;

	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

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

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

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

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

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