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 Solution {
	 
	
	public static void main(String[] args) throws Exception
    {
		FastReader fr=new FastReader();
	    int t=fr.nextInt();
	     while(t-->0) {
	    	long n=fr.nextLong();
	         long a=fr.nextLong();
	    	long b=fr.nextLong();
	    	if(a==1) {
	    		if((n-1)%b==0)
	    			System.out.println("yes");
	    		else
	    			System.out.println("no");
	    	}
	    	else {
	    		boolean pos=false;
	    		long temp=1;
	    	   while(temp<=n) {
	    		   if((n-temp)%b==0)
	    		   {
	    			   pos=true;System.out.println("yes");break;
	    		   }
	    		   else
	    			   temp=temp*a;
	    	   }
	    	   if(!pos)
	    		   System.out.println("no");
	    	}
	        
	     }
    }
	
	public static boolean isPower(long n,long f) {
		
		   double v1=Math.floor(Math.log(n)/Math.log(f));
		   double v2=Math.ceil(Math.log(n)/Math.log(f));
		   return v1==v2;
	}
	
	
	
		
	
	 
public static String lcs(String a,String b) {
		int dp[][]=new int[a.length()+1][b.length()+1];
		for(int i=0;i<=a.length();i++)
		{
			for(int j=0;j<=b.length();j++)
			{
				if(i==0||j==0)
					dp[i][j]=0;
			}
		}
		
		for(int i=1;i<=a.length();i++)
		{
			for(int j=1;j<=b.length();j++)
			{
				if(a.charAt(i-1)==b.charAt(j-1))
					dp[i][j]=1+dp[i-1][j-1];
				else
					dp[i][j]=Math.max(dp[i-1][j],dp[i][j-1]);
			}
		}
		
		int i=a.length();
		int j=b.length();
		String lcs="";
		while(i>0&&j>0)
		{
			if(a.charAt(i-1)==b.charAt(j-1)) {
				lcs=a.charAt(i-1)+lcs;
				i--;
				j--;
			}
			else 
			{
				if(dp[i-1][j]>dp[i][j-1])
					i--;
				else
					j--;
			}
		}
		
		return lcs;
            
	}
	
	 
	 
	 
	 public static long facto(long n) {
		 if(n==1||n==0)
			 return 1;
		 return n*facto(n-1);
	 }
	 public static long gcd(long n1,long n2) {
		 if (n2 == 0) {
		        return n1;
		    }
		    return gcd(n2, n1 % n2);
	}
	 public static boolean isPali(String s) {
		 int i=0;
		 int j=s.length()-1;
		 while(i<=j) {
			 if(s.charAt(i)!=s.charAt(j))
				 return false;
			 i++;
			 j--;
		 }
		 return true;
	 }
	 public static String reverse(String s) {
		 String res="";
		 for(int i=0;i<s.length();i++) {
			 res+=s.charAt(i);
		 }
		 return res;
	 }
	
		
	 
	 public static int bsearch(long suf[],long val) {
		 int i=0;
		 int j=suf.length-1;
		 while(i<=j) {
			 int mid=(i+j)/2;
			 if(suf[mid]==val)
				 return mid;
			 else if(suf[mid]<val)
				 j=mid-1;
			 else
				 i=mid+1;
		 }
		 return -1;
	 }
	 
	 
	 
	
	 
	 
	public static int[] getFreq(String s) {
		int a[]=new int[26];
		for(int i=0;i<s.length();i++) {
			a[s.charAt(i)-'a']++;
		}
		return a;
		
	}
	 
	 public static boolean isPrime(int n) {
		 
		 for(int i=2;(i*i)<=n;i++) {
			 if(n%i==0)
				 return false;
		 }
		 return true;
	 }
            	  
             
             
    }
class Pair implements Comparable<Pair>{
	int start;
	int end;
	Pair(int start,int end){
		this.start=start;
		this.end=end;
	}
	public int compareTo(Pair o) {
		return this.start-o.start;
	}
	
}

	
	 
	
	

	 
 
  

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();
    }
 
    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;
    }
}