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.*;
public class p1095C {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        StringBuilder sb=new StringBuilder();
        int n=sc.nextInt(),k=sc.nextInt(),a[]=new int[k];
        n-=k;
        Arrays.fill(a,1);
        for(int i=0;i<k&&n>0;i++) while(a[i]<=n) {n-=a[i];a[i]*=2;}
        if(n!=0) sb.append("NO");
        else {sb.append("YES\n"); for(int i:a) sb.append(i+" ");}
        System.out.println(sb.toString());
    }
}