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 Main {
	
	public void run () {
		long[] powers = new long[32];
		powers[0] = 1L;
		for (int i = 1; i < powers.length; i++) {
			powers[i] = powers[i - 1] * 2;
			// System.out.println (powers[i]);
		}
		
		Scanner sc = new Scanner (System.in);
		long n = sc.nextLong ();
		int k = sc.nextInt ();
		boolean flag = false;
		
		int[] arr = new int[k];
		long sum = 0;
		for (int i = 0; i < k; i++) {
			arr[i] = 0;
			sum += powers[arr[i]];
		}
		
		int j = 0;
		
		if (sum == n) {
			flag = true;
			System.out.println ("YES");
			System.out.print (powers[arr[0]]);
			for (int i = 1; i < k; i++) {
				System.out.print (" " + powers[arr[i]]);
			}
		} else {
			while (j < k && sum <= n) {
				if (sum + powers[arr[j]] == n) {
					arr[j] ++;
					flag = true;
					System.out.println ("YES");
					System.out.print (powers[arr[0]]);
					for (int i = 1; i < k; i++) {
						System.out.print (" " + powers[arr[i]]);
					}
					break;
				} else if (sum + powers[arr[j]] <= n) {
					sum += powers[arr[j]];
					arr[j] ++;
				} else {
					j++;
				}
			}
		}
		
		
		if (!flag) System.out.println ("NO");
	} 
	
	public static void main (String[] args) {
		new Main ().run ();
	}
	
}