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.ArrayList;
import java.util.Scanner;

public class PowersOfTwo {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		int ones = 0;
		int n1 = n;
		int j=0;
		ArrayList<Integer> a = new ArrayList<Integer>();
		while(n1!=0) {
			if(n1%2==1) {
				ones++;
				a.add((int) Math.round(Math.pow(2, j)));
			}
			n1 = n1>>1;
			j++;
		}
		int[] table = new int[200001];
		for(int i=0;i<ones;i++)
			table[i] = a.get(i);
		if(k>=ones && k<=n) {
			System.out.println("YES");
			int i=0;
			while(ones < k) {
				if(table[i]!=1) {
					table[i] /=2;
					table[ones] = table[i];
					ones++;
				}else i++;
			}
			for(int l=0;l<ones;l++)
				System.out.print(table[l]+" ");
		}
		else {
			System.out.println("NO");
		}

	}

}