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.*;
import java.io.*;

public class Solution {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        String[] ins = br.readLine().trim().split(" ");
        int n = Integer.parseInt(ins[0]);
        int k = Integer.parseInt(ins[1]);
        LinkedList<Integer> list = new LinkedList();
        for(int i=0; i<31; i++) {
            if(((n >> i) & 1) == 1) list.addFirst(1<<i); 
        }
        while(list.size() < k && list.getFirst() != 1) {
            int head = list.removeFirst();
            if(head/2 > 1) {
                list.addFirst(head/2);
                list.addFirst(head/2);
            }
            else {
                list.addLast(1);
                list.addLast(1);
            }
        }
        if(list.size() == k) {
            out.write("YES\n");
            for(int i: list) out.write(i+" ");
        }
        else out.write("NO\n");
        out.flush();
    }
}