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 brefew {
	public static void main(String[] args) {
		Scanner scanny = new Scanner(System.in);
		int n = scanny.nextInt();
		int k = scanny.nextInt();
		String s = Integer.toBinaryString(n);
		int ones = 0;
		for(int i = 0; i < s.length(); i++) if(s.charAt(i)=='1') ones++;
		if(n<k||ones>k) System.out.println("NO");
		else {
			System.out.println("YES");
			int[] arr = new int[35];
			for(int i = 0; i < s.length(); i++) if(s.charAt(i)=='1') arr[s.length()-i-1] ++;
			//System.out.println(Arrays.toString(arr));
			while(ones<k) {
				int last = 34;
				while(arr[last]==0) last--;
				arr[last]--;
				arr[last-1]+=2;
				ones++;
			}
			for(int i = 0; i < 34; i++) {
				if(arr[i]>0) {
					for(int j = 0; j < arr[i]; j++) System.out.print((int)Math.pow(2, i)+" ");
				}
			}
		}
	}
}