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 PowersOfTwo{
	static int n;
	static int k;
	static int[] arr;
	static void getIndex(int a){
		int i = 0;
		while(a > 0){
			arr[i] = a%2;
			a = a/2;
			i++;
		}
	}
	static void finalAnswer(int x){
		if(x==0){
			return;
		}
		else{
			int maxIndex = 0;
			for(int i=0; i<40; i++){
				if(arr[i]!=0){
					maxIndex = i;
				}
			}
			arr[maxIndex-1] += 2;
			arr[maxIndex] -= 1;
			finalAnswer(x-1);
		}
	}
	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		k = sc.nextInt();
		arr = new int[40];
		arr[0] = 0;
		getIndex(n);
		long ways = 0;
		long diff = 0;
		for(int i=0; i<40; i++){
			if(arr[i]!=0){
				ways = ways + (long)Math.pow(2, i);
				diff++;
			}
		}
		if(k<=ways && k>=diff){
			System.out.println("YES");
			int r = k - (int)diff;
			finalAnswer(r);
			for(int i=0; i<40; i++){
				if(arr[i]!=0){
					for(int j=0; j<arr[i]; j++){
						System.out.print((int)Math.pow(2,i)+" ");
					}
				}
			}
			System.out.println("");
		}
		else{
			System.out.println("NO");
		}
	}
}