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.lang.reflect.Array;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.*;



public class copy{
    public static int find(int a,int[] parent)
    {
        if(parent[a]==-1)
            return a;
        return find(parent[a],parent);
    }

    public static void union(int a,int b,int[] parent, int[] rank)
    {
        int x=find(a,parent);
        int y=find(b,parent);
        if(rank[x]>rank[y])
            parent[y]=x;
        else if(rank[y]>rank[x])
            parent[x]=y;
        else
        {
            parent[x]=y;
            rank[y]++;
        }
    }

    static double answer;

    public static int check(ArrayList<ArrayList<Integer>> edges,int x,int parent,int[] statues,int n)
    {
        ArrayList<Integer> arr=new ArrayList<>();
        for(int i:edges.get(x))
        {
            if(i!=parent)
            {
                arr.add(check(edges,i,x,statues,n));
            }
        }
        int sum=0;
        for(int i=arr.size()-1;i>=0;i--)
        {

            answer+=((long)arr.get(i)*(long)sum*(long)statues[x])/((double)n*(double)(n-1));
            sum+=arr.get(i);
        }
        answer+=((long)sum*(long)statues[x])/((double)n*(double)(n-1));
        //System.out.println(x+" "+sum);
        return 1+sum;
    }

        public static boolean check(int X,int a,int b)
    {
        System.out.println(X);

        if(X==1)
            return true;
        boolean status=false;
        if(X%a==0 && a!=1)
            status=status || check(X/a,a,b);
        if(X-b>=1 && b!=0)
            status=status || check(X-b,a,b);

        return status;


    }



    public static void main(String[] args)throws IOException
    {
        Reader.init(System.in);
        BufferedWriter output=new BufferedWriter(new OutputStreamWriter(System.out));
        int T=Reader.nextInt();
        for(int m=1;m<=T;m++)
        {
            long X=Reader.nextLong();
            long a=Reader.nextLong();
            long b=Reader.nextLong();
            long num=1;
            boolean status=false;
            if(a==1) {
                if ((X-1) % b == 0)
                    output.write("YES" + "\n");
                else
                    output.write("NO"+"\n");
            }
            else {
                //System.out.println("hello");
                while (num <= X) {
                    if (num % b == X % b) {
                        output.write("YES" + "\n");
                        status = true;
                        break;
                    }
                    num *= a;
                }
                if (!status)
                    output.write("NO" + "\n");
            }






        }

        output.flush();

    }
}

class cord
{
    int x,y;
    cord(int x1,int y1)
    {
        x=x1;
        y=y1;
    }
}

class cp
{
    int a,b;
    cp(int a,int b)
    {
        this.a=a;
        this.b=b;

    }
}

class sort_cp implements Comparator<cp>
{
    public int compare(cp o1,cp o2)
    {
        if(o1.b>o2.b)
            return -1;
        else if(o1.b<o2.b)
            return 1;
        else
            return 0;
    }
}
class g_node{
    int val;
    long wt;

    g_node(int val, long wt)
    {
        this.val = val;
        this.wt = wt;
    }
}
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}