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.Scanner;
public class Test{
	public static void main (String[] args){
		Scanner cin = new Scanner(System.in);
		int n = cin.nextInt();
		int k=cin.nextInt();
		int sz[] = new int[31];
		sz[0]=1;
		int szz[] = new int[300000];
		for(int i=1;i<=30;i++) {
			sz[i]=2*sz[i-1];
		}
		int num=0;
		for(int i=30;i>=0;i--) {
			while(n-sz[i]>=k-1&&n!=0&&k!=0) {
				n=n-sz[i];
				num++;
				szz[num]=sz[i];
				k--;
			}
		}
		if(n==0) {
			System.out.println("YES");
			for(int i=num;i>1;i--) {
				System.out.print(szz[i]+" ");
			}
			System.out.println(szz[1]);
		}else {
			
		 System.out.println("NO");
		}
	}
}