Problem: A positive integer x is called a power of two if it can be represented as x = 2^y, where y is a non-negative integer. So, the powers of two are 1, 2, 4, 8, 16, ....

You are given two positive integers n and k. Your task is to represent n as the sum of exactly k powers of two.

Input

The only line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 2 ⋅ 10^5).

Output

If it is impossible to represent n as the sum of k powers of two, print NO.

Otherwise, print YES, and then print k positive integers b_1, b_2, ..., b_k such that each of b_i is a power of two, and ∑ _{i = 1}^{k} b_i = n. If there are multiple answers, you may print any of them.

Examples

Input


9 4


Output


YES
1 2 2 4 


Input


8 1


Output


YES
8 


Input


5 1


Output


NO


Input


3 7


Output


NO

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.*;
public class Main
{
  static int a[];
  static int func(int x){
    int i=0,ret=1;
    for(i=0;i<31;i++){
		ret=a[i];
		if(x<ret)
     return a[i-1];
     }
     return a[i-1];
  }
    public static void main(String[] args)throws IOException
    {
        FastReader in=new FastReader(System.in);
        StringBuffer st=new StringBuffer();
        a=new int[32];
        int put=1;
        for(int i=0;i<31;i++){
        a[i]=put;
		    put+=put;
        }
        int n=in.nextInt(),k=in.nextInt();
        ArrayList<Integer> v=new ArrayList<>();
        if(n<k)
        st.append("NO\n");
        else{
          while(true){
				  if(n<=0 || k<=0) 
          break;
			  	int tar=n-k+1;
				  int f=func(tar);
			  	v.add(f);
			  	n-=f;
				  k--;
			 }
			  if(n==0){
				st.append("YES\n");
				int i,sz=v.size();
				for(i=sz-1;i>=0;i--)
				{
					st.append(v.get(i)+" ");
				}
				
			}
			else 
      st.append("NO\n");
 
        }
        
        
        
          
        System.out.print(st);
    }
    static class FastReader{
 
        byte[] buf = new byte[2048];
        int index, total;
        InputStream in;
 
        FastReader(InputStream is) {
            in = is;
        }
 
        int scan() throws IOException {
            if (index >= total) {
                index = 0;
                total = in.read(buf);
                if (total <= 0) {
                    return -1;
                }
            }
            return buf[index++];
        }
 
        String next() throws IOException {
            int c;
            for (c = scan(); c <= 32; c = scan());
            StringBuilder sb = new StringBuilder();
            for (; c > 32; c = scan()) {
                sb.append((char) c);
            }
            return sb.toString();
        }
 
        int nextInt() throws IOException {
            int c, val = 0;
            for (c = scan(); c <= 32; c = scan());
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
 
        long nextLong() throws IOException {
            int c;
            long val = 0;
            for (c = scan(); c <= 32; c = scan());
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
    }
}