Vanya has a scales for weighing loads and weights of masses w0, w1, w2, ..., w100 grams where w is some integer not less than 2 (exactly one weight of each nominal value). Vanya wonders whether he can weight an item with mass m using the given weights, if the weights can be put on both pans of the scales. Formally speaking, your task is to determine whether it is possible to place an item of mass m and some weights on the left pan of the scales, and some weights on the right pan of the scales so that the pans of the scales were in balance.

Input

The first line contains two integers w, m (2 ≤ w ≤ 109, 1 ≤ m ≤ 109) — the number defining the masses of the weights and the mass of the item.

Output

Print word 'YES' if the item can be weighted and 'NO' if it cannot.

Examples

Input

3 7


Output

YES


Input

100 99


Output

YES


Input

100 50


Output

NO

Note

Note to the first sample test. One pan can have an item of mass 7 and a weight of mass 3, and the second pan can have two weights of masses 9 and 1, correspondingly. Then 7 + 3 = 9 + 1.

Note to the second sample test. One pan of the scales can have an item of mass 99 and the weight of mass 1, and the second pan can have the weight of mass 100.

Note to the third sample test. It is impossible to measure the weight of the item in the manner described in the input. 
	import java.util.*;
	import java.io.*;
	import java.math.*;
	public class Main {
		public static long mod= (long) (1e9 +7);
		public static void main(String args[])
		{
			InputReader s= new InputReader(System.in);
			OutputStream outputStream= System.out;
			PrintWriter out= new PrintWriter(outputStream);
			int w= s.nextInt();
			int m= s.nextInt();
			 if (w <= 3)
		            out.println("YES");
		        else {
		            while (m != 0) {
		                if (m % w != (w - 1) && m % w != 0 && m % w != 1) {
		                    System.out.println("NO");
		                    return;
		                }
		                m = (m + 1) / w;
		            }
		            out.println("YES");
		        }
			out.close();
		}
		
		static long combinations(long n,long r){   // O(r)
			if(r==0 || r==n) return 1;
			r= Math.min(r, n-r);
			long ans=n;  // nC1=n;
			for(int i=1;i<r;i++){
				ans= ans*(n-i);
				ans= ans/(i+1);
			}
			return ans;
			
		}
		public static void debug(Object... o) {
			System.out.println(Arrays.deepToString(o));
		}
		static long modulo(long a,long b,long c) {
			long x=1;
			long y=a;
			while(b > 0){
				if(b%2 == 1){
					x=(x*y)%c;
				}
				y = (y*y)%c; // squaring the base
				b /= 2;
			}
			return  x%c;
		}
		static void catalan_numbers(int n) {
			long catalan[]= new long[n+1];
		    catalan[1] = 1;
		    for (int i = 2; i <= n; i++) {
		        for (int j = 1; j <= i - 1; j++) {
		            catalan[i] = catalan[i] + ((catalan[j]) * catalan[i - j]);
		        }
		    }
		}
		
		static ArrayList<Integer> primeFactors(int n)   // O(sqrt(n))
		{
		    // Print the number of 2s that divide n
			ArrayList<Integer> arr= new ArrayList<>();
		    while (n%2 == 0)
		    {
		        arr.add(2);
		        n = n/2;
		    }
		 
		    // n must be odd at this point.  So we can skip one element (Note i = i +2)
		    for (int i = 3; i <= Math.sqrt(n); i = i+2)
		    {
		        // While i divides n, print i and divide n
		        while (n%i == 0)
		        {
		            arr.add(i);
		            n = n/i;
		        }
		    }
		    // This condition is to handle the case when n is a prime number
		    // greater than 2
		    if (n > 2)
		        arr.add(n);
		    
		    return arr;
		}
	
		public static int expo(int a, int b){
			if (b==0)
		        return 1;
		    if (b==1)
		        return a;
		    if (b==2)
		        return a*a;
	
		    if (b%2==0){
		            return expo(expo(a,b/2),2);
		    }
		    else{
		        return a*expo(expo(a,(b-1)/2),2);
		    }
		}
		static class Pair implements Comparable<Pair>
		{
			int f;
			int s;
			Pair(int ii, int cc)
			{
				f=ii;
				s=cc;
			}
			
			public int compareTo(Pair o) 
			{
				return Integer.compare(this.f, o.f);
			}
			
		}
		
		public static int[] sieve(int N){    // O(n*log(logn))
			int arr[]= new int[N+1];
			for(int i=2;i<=Math.sqrt(N);i++){
				if(arr[i]==0){
					for(int j= i*i;j<= N;j= j+i){
						arr[j]=1;
					}
				}
			}
			return arr;
			// All the i for which arr[i]==0 are prime numbers.
		}
		static long gcd(long a,long b){       // O(logn)
			if(b==0) return a;
			return gcd(b,a%b);
		}
		static class InputReader {
	
		    public BufferedReader reader;
		    public StringTokenizer tokenizer;
	 
		    public InputReader(InputStream inputstream) {
		      reader = new BufferedReader(new InputStreamReader(inputstream));
		      tokenizer = null;
		    }
		    
		    public String nextLine(){
		    	String fullLine=null;
		    	while (tokenizer == null || !tokenizer.hasMoreTokens()) {
		            try {
		              fullLine=reader.readLine();
		            } catch (IOException e) {
		              throw new RuntimeException(e);
		            }
		            return fullLine;
		          }
		          return fullLine;
		    }
			public String next() {
		      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
		        try {
		          tokenizer = new StringTokenizer(reader.readLine());
		        } catch (IOException e) {
		          throw new RuntimeException(e);
		        }
		      }
		      return tokenizer.nextToken();
		    }
			public long nextLong() {
			      return Long.parseLong(next());
			    }
		    public int nextInt() {
		      return Integer.parseInt(next());
		    }
		  }
	}