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.util.*;
import java.util.Arrays;
import java.lang.Math;


public class Main {

    public static void main(String[] args) {
	    Scanner sc = new Scanner(System.in);
	    long n = sc.nextLong();
		int k = sc.nextInt();
		long x = k;
		long[] vetor = new long[k+k];
		Arrays.fill(vetor, 1);
		int i;
		for(i=0;i<=k-1;i++){
			while(x+vetor[i]<=n) {
				x += vetor[i];
				vetor[i] *= 2;
			}
		}
		if(x!=n || k>n) {
			System.out.println("NO");
		}else{
			System.out.println("YES");
			i=0;
			while(i<k){
				System.out.print(vetor[i]+" ");
				i++;
			}
		}
    }
}