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 PowerOfTwo {
	
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int k = s.nextInt();
		Stack<Integer> arr = new Stack<>();
		int setbit = 0;
		for(int i=0;i<=31;i++) {
			if((n&(1<<i))!=0) {
				arr.add(1<<i);
				setbit++;
			}
		}
	//	System.out.println(arr);
		int count = 0;
		for(int i=0;i<arr.size();i++) {
			count+=arr.get(i);
		}
		if(setbit>k ||count<k) {
			System.out.println("NO");
		}
		else if(k==setbit) {
			System.out.println("YES");
			for(int m:arr) {
				System.out.print(m+" ");
			}
			System.out.println();
		}
		else if(k==n) {
			System.out.println("YES");
			for(int i=0;i<k;i++) {
				System.out.print(1+" ");
			}
			System.out.println();
		}
		else {
			Stack<Integer> storeOne = new Stack<>();
			System.out.println("YES");
			int c = arr.size();
			while(storeOne.size()+arr.size()<k && !arr.isEmpty()) {
				int q = arr.pop();;
				if(q==1) {
					storeOne.push(q);
				}
		//		System.out.println(q);
				if(q/2>=1) {
					arr.push(q/2);
					arr.push(q/2);
				}
				c++;
			}
		//	System.out.println(arr.size());
			while(!storeOne.isEmpty()) {
				System.out.print(storeOne.pop()+" ");
			}
			while(!arr.isEmpty()) {
				System.out.print(arr.pop()+" ");
			}
			System.out.println();
		}
	}

	

}