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 POT {
    public static void main(String args[]) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt() , k = scan.nextInt();
        if(Integer.bitCount(n) > k){
            System.out.println("NO");
            return;
        }
        int[] arr = new int[32];
        PriorityQueue<Integer> q = new PriorityQueue<>(Collections.reverseOrder());
        for(int i = 0 ; i < 32 ; i++){
            if(((1 << i) & n) != 0){
                q.add(i);
                arr[i]++;
            }
        }
        int cnt = q.size();
        while(cnt < k && q.size() > 0){
            int top = q.poll();
            if(top > 0){
                arr[top]--;
                arr[top - 1]+=2;
            }
            if(top  > 0){
                q.addAll(Arrays.asList(top-1,top-1));
                cnt++;
            }
        }
        if(cnt != k){
            System.out.println("NO");
            return;
        }
        System.out.println("YES");
        for(int i = 0 ; i < 32 ; i++){
            while(arr[i]-- > 0){
                System.out.print((1 << i) + " ");
            }
        }
        
    }
}