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.*;
import java.io.*;

public class Solution {

	public static void main(String[] args) {
		Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		int num = in.nextInt();
		int k = in.nextInt();
		int tmp = num;
		ArrayList<Integer> list = new ArrayList();
		int count = 0;
		while (num != 0) {
			if ((num & 1) == 1)
				list.add(count);
			count++;
			num >>>= 1;
		}
		if(k < list.size() || k > tmp) {
			System.out.println("NO");
			return;
		}else {
			System.out.println("YES");
		}
		int[] pow = new int[31];
		int val = 1;
		for(int x = 0; x < 31; x++) {
			pow[x] = val;
			val *= 2;
		}
		k -= list.size();
		
		for(int x = list.size() - 1; x >= 0; x--) {
			k++;
			int ele = pow[list.get(x)];
			if(k == 1)
			{
				System.out.print(ele + " ");
				k--;
				continue;
			}
			if(k >= ele) {
				for (int i = 0; i < ele; i++) {
					System.out.print(1 + " ");
				}
				k -= ele;
			}
			else {
				while(k != 0) {
					if(k == 1) {
						System.out.print(ele + " ");
						break;
					}
					ele /= 2;
					if(ele < k) {
						for (int i = 0; i < ele; i++) {
							System.out.print(1 + " ");
						}
						k -= ele;
					}
					else {
						System.out.print(ele + " ");
						k--;
					}
				}
				k = 0;
			}
		}
	}

}