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 Main {
	public static int cnt(int x) {
		int ret=0;
		while (x>0) {
			x-=x&-x;
			++ret;
		}
		return ret;
	}
	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		int n=in.nextInt();
		int k=in.nextInt();
		int m=cnt(n);
		if (k<m||n<k) System.out.println("NO");
		else {
			System.out.println("YES");
			int[] que=new int[k+k];
			int st=0,ed=0;
			for (int i=0;i<31;++i)
				if ((n>>i&1)==1) que[ed++]=i;
			while (ed-st<k) {
				int u=que[st++];
				if (u==0) {
					--k;
					System.out.printf("%d ",1);
				} else {
					que[ed++]=u-1;
					que[ed++]=u-1;
				}
			}
			for (int i=st;i<ed;++i)
				System.out.printf("%d ",1<<que[i]);
		}
	}
}