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:

 
 //   * * * the goal is to be worlds best * * *   //
 import java.io.BufferedReader;
 import java.io.IOException;
 import java.io.InputStreamReader;
 import java.util.*;
  
 
 public class B {
     static class Pair implements Comparable<Pair>{
         int a;
         int b;
 
         Pair(int a , int b){
             this.a = a;
             this.b = b;
         }
 
         public int compareTo(Pair o){
             return this.a - o.a;
         }
     }
 
 //==================================================================================================
 
     public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int t = sc.nextInt();
        while(t-->0){
            long n = sc.nextLong();
            long a = sc.nextLong();
            long b = sc.nextLong();

            if(a == 1){
                if((n - 1) % b != 0){
                    System.out.println("No");
                }
                else{
                    System.out.println("Yes");
                }
                continue;
            }

            boolean found = true;
            long i = 1L;
            while(i < n + 1){
                if((n - i) % b == 0){
                    found = false;
                    break;
                }
                i *= a;
            }
    
            if(!found){
                System.out.println("Yes");
                continue;
            }
            System.out.println("No");
        }
     }
 
 //==================================================================================================
 
 
     // Use this instead of Arrays.sort() on an array of ints. Arrays.sort() is n^2
     // worst case since it uses a version of quicksort. Although this would never
     // actually show up in the real world, in codeforces, people can hack, so
     // this is needed. 
	 static void sort(int[] arr) {
		 int n = arr.length;
		 ArrayList<Integer> res = new ArrayList<>();
		 for (int a : arr) {
		 	 res.add(a);
		 }
		 Collections.sort(res);
		 for (int i = 0; i < n; i++) {
			 arr[i] = res.get(i);
		 }
	 }
 
	 static void sort(long[] arr) {
		 int n = arr.length;
		 ArrayList<Long> res = new ArrayList<>();
		 for (long a : arr) {
			 res.add(a);
		 }
		 Collections.sort(res);
		 for (int i = 0; i < n; i++) {
			 arr[i] = res.get(i);
		} 
	 }
 
	 static void revSort(int[] arr) {
		 int n = arr.length;
		 ArrayList<Integer> res = new ArrayList<>();
		 for (int a : arr) {
			 res.add(a);
		 }
		 Collections.sort(res, Collections.reverseOrder());
		 for (int i = 0; i < n; i++) {
			 arr[i] = res.get(i);
		 }
	 } 
     
     // Use this to input code since it is faster than a Scanner
     static class FastScanner {
         BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
         StringTokenizer st=new StringTokenizer("");
         String next() {
             while (!st.hasMoreTokens())
                 try {
                     st=new StringTokenizer(br.readLine());
                 } catch (IOException e) {
                     e.printStackTrace();
                 }
             return st.nextToken();
         }
         
         int nextInt() {
             return Integer.parseInt(next());
         }
 
         double nextDouble() {
             return Double.parseDouble(next());
         }
  
         String str = "";
  
         String nextLine() {
             try {
                 str = br.readLine();
             } catch (IOException e) {
                 e.printStackTrace();
             }
             return str;
         }
  
         int[] readArray(int n) {
             int[] a = new int[n];
             for (int i = 0; i < n; i++)
                 a[i] = nextInt();
             return a;
         }
  
         long[] readLongArray(int n) {
             long[] a = new long[n];
             for (int i = 0; i < n; i++)
                 a[i] = nextLong();
             return a;
         }
         long nextLong() {
             return Long.parseLong(next());
         }
     }
     
     // print integers in array
     static void print(int a[]){
         for(int e : a){
             System.out.print(e + " ");
         }
         System.out.println();
     }

     static void print(long a[]){
         for(long e : a){
             System.out.print(e + " ");
         }
         System.out.println();
     }

     // generates all the prime numbers upto n
     static void sieveOfEratosthenes(int n , ArrayList<Integer> al)
     {
         boolean prime[] = new boolean[n + 1];
         for (int i = 0; i <= n; i++)
             prime[i] = true;
  
         for (int p = 2; p * p <= n; p++) 
         {
             if (prime[p] == true) 
             {
                 for (int i = p * p; i <= n; i += p)
                     prime[i] = false;
             }
         }
         for (int i = 2; i <= n; i++)
         {
             if (prime[i] == true)
                 al.add(i);
         }
     }
     static final int mod = 1000_000_000 + 7;
     static final int imx = Integer.MAX_VALUE;
     static final int imi = Integer.MIN_VALUE;
     
	 static ArrayList<Integer> divisors(int n) {
		 ArrayList<Integer> al = new ArrayList<>();
		 for (int i = 1; i * i <= n; i++) {
			 if (n % i == 0) {
				 if (n == i * i) {
					 al.add(i);
				 } else {
					 al.add(i);
					 al.add(n / i);
				 }
		 	 }
		 }
		 Collections.sort(al);
		 return al;
	 }
 
	 static int countDigits(int n) {
		 int c = 0;
		 while (n != 0) {
			 c++;
			 n /= 10;
		 }
		 return c;
	 }
 
	 static boolean palindrome(String str) {
		 int s = 0;
		 int e = str.length() - 1;
		 while (s < e) {
			 if (str.charAt(s) != str.charAt(e)) {
				 return false;
			 }
			 s++;
			 e--;
		 }
		 return true;
	 }
 
	 static void reverse(int[] arr, int s, int e) {
		 while (s < e) {
			 int temp = arr[s];
			 arr[s++] = arr[e];
			 arr[e--] = temp;
		 }
	 }
     // starting exclusive ending inclusive
	 static int getMax(int[] arr, int s, int e) {
		 int maxi = s;
		 for (int i = s + 1; i <= e; i++) {
			 if (arr[i] > arr[maxi]) {
				 maxi = i;
			 }
		 }
		 return maxi;
	 }

     // starting exclusive ending inclusive
     static int getMin(int[] arr, int s, int e) {
	     int mini = s;
		 for (int i = s + 1; i <= e; i++) {
			 if (arr[i] < arr[mini]) {
				 mini = i;
			 }
		 }
		 return mini;
	 }
 
	 static long lcm(long n1, long n2) {
		 return (n1 * n2) / gcd(n1, n2);
 	 }
 
	 static int lcm(int n1, int n2) {
		 return (n1 * n2) / gcd(n1, n2);
	 }
 
	 static long gcd(long num1, long num2) {
		 if (num2 == 0) {
			 return num1;
		 }
		 return gcd(num2, num1 % num2);
	 }
 
	 static int gcd(int num1, int num2) {
		 if (num2 == 0) {
			 return num1;
		 }
		 return gcd(num2, num1 % num2);
	 }

     //fastPow
     static long fastPow(long base, long exp) {
         if (exp==0) return 1;
         long half=fastPow(base, exp/2);
         if (exp%2==0) return mul(half, half);
         return mul(half, mul(half, base));
     }
 
     // multiply two long numbers % mod
     static long mul(long a, long b) {
         return a*b%mod;
     }
 
     static int nCr(int n, int r)
     {
        return factorial(n) / (factorial(r) *
            factorial(n - r));
     }
     
     // Returns factorial of n
     static int factorial(int n)
     {
         int res = 1;
         for (int i = 2; i <= n; i++)
             res = res * i;
         return res;
     }
      
     // to generate the lps array
     // lps means longest preffix that is also a suffix
     static void generateLPS(int lps[] , String p){
         int l = 0;
         int r = 1;
    
         while(l < p.length() && l < r && r < p.length()){
             if(p.charAt(l) == p.charAt(r)){
                 lps[r] = l + 1;
                 l++;
                 r++;
             }
             else{
                 if(l > 0)
                     l = lps[l - 1];
                 else
                     r++;    
             }
         }
     }
      
     // returns the index of the element which is just smaller than or
     // equal to the tar in the given arraylist 
     static int lowBound(ArrayList<Integer> ll,long tar ,int l,int r){
         if(l>r) return l;
 
         int mid=l+(r-l)/2;
 
         if(ll.get(mid)>=tar){
             return lowBound(ll,tar,l,mid-1);
         }
 
         return lowBound(ll,tar,mid+1,r);
     }
 
     // returns the index of the element which is just greater than or
     // equal to the tar in the given arraylist 
     static int upBound(ArrayList<Integer> ll,long tar,int l ,int r){
         if(l>r) return l;
 
         int mid=l+(r-l)/2;
 
         if(ll.get(mid)<=tar){
             return upBound(ll,tar,mid+1 ,r);
         }
 
         return upBound(ll,tar,l,mid-1);
     }
 
     static void swap(int a[] , int i , int j){
         int x = a[i];
         int y = a[j];
         a[j] = x;
         a[i] = y;
     }
     static void swap(long a[] , int i , int j){
         long x = a[i];
         long y = a[j];
         a[j] = x;
         a[i] = y;
    }
     // a -> z == 97 -> 122
 
     // String.format("%.9f", ans) ,--> to get upto 9 decimal places , (ans is double)
     
     // write 
 }