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:
//package Codeforces;
import java.util.*;

public class powers01 {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		long n = in.nextInt();
		long k = in.nextInt();
		if(k > n) {
			System.out.println("NO");
		}
		else {
			char[] bin = Long.toBinaryString(n).toCharArray();
			int cnt = 0;
			PriorityQueue<Long> pq = new PriorityQueue<Long>(Collections.reverseOrder());
			long pow = bin.length-1;
			for(int i=0; i<bin.length; i++) {
				if(bin[i] == '1') {
					cnt++;
					pq.add((long) (1<<pow));
				}
				pow--;
			}
			if(cnt > k || k == 1 && cnt !=1) {
				System.out.println("NO");
			}
			else {
				if(cnt == k) {
					System.out.println("YES");
					for(Long i: pq)
						System.out.print(i+" ");
				}
				else {
					while(cnt != k) {
						long tmp = pq.poll();
						pq.add((long) tmp/2);
						pq.add((long) tmp/2);
						cnt+=1;
					}
					System.out.println("YES");
					for(Long i: pq)
						System.out.print(i+" ");
				}
				
			}
		 
		}
	}
}