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.*;
public class Main {
	
	
	
//    ***                          ++                      
// +=-==+                      +++=-                     
//+-:---==+                   *+=----=                   
//+-:------==+               ++=------==                  
//=-----------=++=========================                
//+--:::::---:-----============-=======+++====             
//+---:..:----::-===============-======+++++++++           
//=---:...---:-===================---===++++++++++         
//+----:...:-=======================--==+++++++++++        
//+-:------====================++===---==++++===+++++      
//+=-----======================+++++==---==+==-::=++**+     
//+=-----================---=======++=========::.:-+*****    
//+==::-====================--:  --:-====++=+===:..-=+*****   
//+=---=====================-...  :=..:-=+++++++++===++*****  
//+=---=====+=++++++++++++++++=-:::::-====+++++++++++++*****+ 
//+=======++++++++++++=+++++++============++++++=======+****** 
//+=====+++++++++++++++++++++++++==++++==++++++=:...  . .+**** 
//++====++++++++++++++++++++++++++++++++++++++++-.     ..-+**** 
//+======++++++++++++++++++++++++++++++++===+====:.    ..:=++++ 
//+===--=====+++++++++++++++++++++++++++=========-::....::-=++* 
//====--==========+++++++==+++===++++===========--:::....:=++*  
//====---===++++=====++++++==+++=======-::--===-:.  ....:-+++   
//==--=--====++++++++==+++++++++++======--::::...::::::-=+++    
//===----===++++++++++++++++++++============--=-==----==+++     
//=--------====++++++++++++++++=====================+++++++     
//=---------=======++++++++====+++=================++++++++     
//-----------========+++++++++++++++=================+++++++    
//=----------==========++++++++++=====================++++++++  
//=====------==============+++++++===================+++==+++++ 
//=======------==========================================++++++

// created by : pritam kumar

    static long LowerBound(long[] a2, long x) { // x is the target value or key
  int l=-1,r=a2.length;
  while(l+1<r) {
    int m=(l+r)>>>1;
    if(a2[m]>=x) r=m;
    else l=m;
  }
  return r;
}
static int UpperBound(int a[], int x) {// x is the key or target value
    int l=-1,r=a.length;
    while(l+1<r) {
       int m=(l+r)>>>1;
       if(a[m]<=x) l=m;
       else r=m;
    }
    return l+1;
 }
    static void ruffleSort(long[] a) {
		int n=a.length;
		Random r=new Random();
		for (int i=0; i<a.length; i++) {
			long oi=r.nextInt(n), temp=a[i];
			a[i]=a[(int)oi];
			a[(int)oi]=temp;
		}
		Arrays.sort(a);
	}
static void ruffleSort(int[] a) {
		int n=a.length;
		Random r=new Random();
		for (int i=0; i<a.length; i++) {
			int oi=r.nextInt(n), temp=a[i];
			a[i]=a[oi];
			a[oi]=temp;
		}
		Arrays.sort(a);
	}
    public static int findIndex(long arr[], long t) 
    { 
 
        // if array is Null 
        if (arr == null) { 
            return -1; 
        } 
 
        // find length of array 
        int len = arr.length; 
        int i = 0; 
 
        // traverse in the array 
        while (i < len) { 
 
            // if the i-th element is t 
            // then return the index 
            if (arr[i] == t) { 
                return i; 
            } 
            else { 
                i = i + 1; 
            } 
        } 
        return -1; 
    }
 
    static int gcd(int a, int b)
    {
        if (a == 0)
            return b; 
        return gcd(b % a, a); 
    }
 
    // method to return LCM of two numbers
    static int lcm(int a, int b)
    {
        return (a / gcd(a, b)) * b;
    }
 
    public static int[] swap(int a[], int left, int right)
    {
 
        // Swap the data
        int temp = a[left];
        a[left] = a[right];
        a[right] = temp;
 
        // Return the updated array
        return a;
    }
//    public static pair swap(long max0,long max1)
//    {
//    	pair p=new pair(0, 0);
//    	long temp=max0;
//    	max0=max1;
//    	max1=temp;
//    	p.x=max0;
//    	p.y=max1;
//    	return p;
//    	
//    }
    public static void swap(int max0,int max1)
    {
    	int temp=max0;
    	max0=max1;
    	max1=temp;
    }
 
    public static int[] reverse(int a[], int left, int right)
    {
 
        // Reverse the sub-array
        while (left < right) {
            int temp = a[left];
            a[left++] = a[right];
            a[right--] = temp;
        }
 
        // Return the updated array
        return a;
    }
 
  
	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;
        }
    } 
	static boolean prime[] ;
		static void sieve(int n)
		{
			prime= new boolean[n+1];
	        for (int i = 0; i <= n; i++)
	            prime[i] = true;
	        prime[0]=false;
	        prime[1]=false;
	        for (int p = 2; p * p <= n; p++)
	        {
	            if (prime[p] == true)
	            {
	                for (int i = p * p; i <= n; i += p)
	                    prime[i] = false;
	            }
	        }
	    }
	    static long[][] a;
	    static ArrayList<Integer>[] tree;
	    static long[][] dp;
	    static void bin(int n)
	    {
	        if (n > 1)
	            bin(n / 2);
	        System.out.print(n % 2);
	    }
	public static void main(String[] args) {
		FastReader s=new FastReader();
		int t=s.nextInt();
		while(t-->0)
		{
			Queue<Long>q=new LinkedList<>();
			long n=s.nextLong();
			long a=s.nextLong();
			long b=s.nextLong();
			boolean flag=true;
			if(a==1)
			{
				if((n-1)%b==0)
				{
					System.out.println("Yes");
				}
				else System.out.println("No");
			}
			else
			{
				long temp=1;
				while(temp<=n)
				{
					if((n-temp)%b==0)
					{
						System.out.println("Yes");
						flag=false;
						break;
					}
					temp*=a;
				}
				if(flag)System.out.println("No");
			}
			
		}
	}
 
	private static boolean isps(int x) {
		if(x>=0)
		{
			long sr=(long)Math.sqrt(x);
			return (sr*sr==x);
		}
		return false;
	}
	private static boolean solver(int[]arr,int n,int sum,boolean[][] mat)
    {
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=sum;j++)
            {
                if(arr[i-1]<=j)
                {
                    mat[i][j]=mat[i-1][j-arr[i-1]]||mat[i-1][j];
                }
                else mat[i][j]=mat[i-1][j];
            }
        }
        return mat[n][sum];
    }
	static void dfs(int v, int p){
        dp[0][v] = 0;
        dp[1][v]=0;
 
        for(int u: tree[v])
        {
            if(u!=p) {
 
 
                dfs(u, v);
                dp[0][v] += Math.max(Math.abs(a[0][v] - a[1][u]) + dp[1][u], Math.abs(a[0][v] - a[0][u]) + dp[0][u]);
                dp[1][v] += Math.max(Math.abs(a[1][v] - a[1][u]) + dp[1][u], Math.abs(a[1][v] - a[0][u]) + dp[0][u]);
            }
 
 
        }
    }
}
class pair{
	long x;
	long y;
	public pair(long x,long y)
	{
		this.x=x;
		this.y=y;
	}
}