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 C {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		String s = Integer.toString(n,2);
			int[] a = new int[s.length()];
			int sum = 0;
			for(int i=0;i<s.length();i++) {
				if(s.charAt(i)=='1') {
					a[i] = 1;
					sum++;
				}
			}
			if(k>=sum&&k<=n) {
				System.out.println("YES");
			while(sum<k) {
				for(int i=s.length()-2;i>=0;i--) {
					if(a[i]>0) {
						a[i]--;
						a[i+1]+=2;
						sum++;
						break;
					}
				}
				//System.out.println(sum);
			}
			for(int i=0;i<s.length();i++) {
				for(int j=0;j<a[i];j++) {
					System.out.print((int)Math.pow(2, s.length()-1-i)+" ");
				}
			}
			System.out.println();
			}else {
				System.out.println("NO");
			}
	}
}