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.io.File;
import java.io.*;
import java.util.*;

public class Main {

    // static final File ip = new File("input.txt");
    // static final File op = new File("output.txt");
    // static {
    // try {
    // System.setOut(new PrintStream(op));
    // System.setIn(new FileInputStream(ip));
    // } catch (Exception e) {
    // }
    // }
    

    public static void main(String[] args) {
      FastReader sc = new FastReader();   
      int test = sc.nextInt();
      while(test-- != 0)
      {
          Long n = sc.nextLong();
          Long a = sc.nextLong();
          Long b = sc.nextLong();
          if(a==1)
          {
              if((n-1)%b == 0)
              System.out.println("YES");
              else
              System.out.println("NO");
              continue;
          }
          long s = 1,f=0;
          while(s <= n)
          {
              if((n-s)%b == 0)
              {
                f = 1;
                break;
              }
              s = s * a;
          }
          if(f==1)
          System.out.println("YES");
          else
          System.out.println("NO");
      }
}

    static long power(long x, long y, long p) {
        long res = 1;
        x = x % p;
        if (x == 0)
            return 0;
        while (y > 0) {
            if ((y & 1) != 0)
                res = (res * x) % p;
            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }

    public static int countSetBits(long number) {
        int count = 0;
        while (number > 0) {
            ++count;
            number &= number - 1;
        }
        return count;
    }

    private static <T> void swap(T[] array, int i, int j) {
        if (i != j) {
            T tmp = array[i];
            array[i] = array[j];
            array[j] = tmp;
        }
    }

    private static long getSum(int[] array) {
        long sum = 0;
        for (int value : array) {
            sum += value;
        }
        return sum;
    }

    private static boolean isPrime(Long x) {
        if (x < 2)
            return false;
        for (long d = 2; d * d <= x; ++d) {
            if (x % d == 0)
                return false;
        }
        return true;
    }

    private static boolean isPrimeInt(int x) {
        if (x < 2)
            return false;
        for (int d = 2; d * d <= x; ++d) {
            if (x % d == 0)
                return false;
        }
        return true;
    }

    private static int[] getPrimes(int n) {
        boolean[] used = new boolean[n + 1];
        used[0] = used[1] = true;
        int size = 0;
        for (int i = 2; i <= n; ++i) {
            if (!used[i]) {
                ++size;
                for (int j = 2 * i; j <= n; j += i) {
                    used[j] = true;
                }
            }
        }
        int[] primes = new int[size];
        for (int i = 0, cur = 0; i <= n; ++i) {
            if (!used[i]) {
                primes[cur++] = i;
            }
        }
        return primes;
    }

    private static long lcm(long a, long b) {
        return a / gcd(a, b) * b;
    }

    private static long gcd(long a, long b) {
        return (a == 0 ? b : gcd(b % a, a));
    }

    static void shuffleArray(int[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for (int i = 0; i < n; ++i) {
            int tmp = arr[i];
            int randomPos = i + rnd.nextInt(n - i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
    }

    static void shuffleList(ArrayList<Long> arr) {
        int n = arr.size();
        Random rnd = new Random();
        for (int i = 0; i < n; ++i) {
            long tmp = arr.get(i);
            int randomPos = i + rnd.nextInt(n - i);
            arr.set(i, arr.get(randomPos));
            arr.set(randomPos, tmp);
        }
    }

    static void factorize(long n) {
        int count = 0;
        while (!(n % 2 > 0)) {
            n >>= 1;

            count++;
        }
        if (count > 0) {
            // System.out.println("2" + " " + count);
        }
        for (long i = 3; i <= (long) Math.sqrt(n); i += 2) {
            count = 0;
            while (n % i == 0) {
                count++;
                n = n / i;
            }
            if (count > 0) {
                // System.out.println(i + " " + count);
            }
        }

        if (n > 2) {
            // System.out.println(i + " " + count);
        }
    }

    static void shuffleArrayL(long[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for (int i = 0; i < n; ++i) {
            long tmp = arr[i];
            int randomPos = i + rnd.nextInt(n - i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public boolean hasNext() {
            return false;
        }

        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;
        }
    }
}