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.util.*;


import java.io.*;
 
/* Name of the class has to be "Main" only if the class is public. */
public class final2
{
	static class Pair{
    	int a;
    	int b;
    	
    }
    static 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; 
        } 
    } 
	public static int gcd(int a, int b)
	{
		if (b == 0)
	        return a;
	    return gcd(b, a % b);
	}
	public static void main (String[] args) throws java.lang.Exception


    {
		 /*Arrays.sort(time,new Comparator<Pair>(){
 			public int compare(Pair p1,Pair p2){
 				if(p1.a==p2.a)
 					return p1.b-p2.b;
 				return p1.a-p2.a;
 			}
 		});*/
	    
			//Your Solve
		FastReader sc = new FastReader();

        int t=sc.nextInt();
        PrintWriter out=new PrintWriter(System.out);
        
        Set<String> st1=new HashSet<String>();
        int i,j,a,b=4,c,d,k,l,r;
        
        long count=0;
        int m,n;
        long sum1=1,sum=0;
        long min,max,y,z;
        long x=0;
        int pos=1;  
        String s="",s1="";
        //ArrayList<Integer> arr=new ArrayList<Integer>();
        //ArrayList<Integer> arr1=new ArrayList<Integer>();
        Set<Integer> st=new HashSet<Integer>();
        //Map<Integer,Integer> hm=new HashMap<Integer,Integer>();
       // int arr[]=new int [26];
        for(;t>0;t--)
        {
        	n=sc.nextInt();
        	a=sc.nextInt();
        	b=sc.nextInt();
        	sum=1;
        	boolean f=false;
        	if(a==1)
        	{
        		if((n-1)%b==0)
            		out.println("YES");
            	else
            		out.println("NO");
        	}
        	else if(b==1)
        		out.println("YES");
        		
        	else
        	{
	        	while(sum<=n)
	        	{
	        		if((n-sum)%b==0)
	        		{
	        			f=true;
	        			break;
	        		}
	        		else
	        		 sum*=(long)a;
	        	}
	        	if(f)
	        		out.println("YES");
	        	else
	        		out.println("NO");
        	}
        }
        	
        
        out.close();
        
    
        
		
        
        
    }
}