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 {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int k = in.nextInt();
        Map<Integer, Integer> map = new HashMap<>();
        Queue<Integer> queue = new LinkedList<>();
        int cnt = 0;
        for (int i = 0; i <= 30; i++) {
            if ((n & (1 << i)) != 0) {
                if (i != 0) {
                    ((LinkedList<Integer>) queue).add(1<<i);
                }
                map.put(1 << i, 1);
                cnt++;
            }
        }
        if (cnt > k) {
            System.out.println("NO");
            return;
        }
        while (cnt < k && !queue.isEmpty()) {
            int z = queue.poll();
            int t = map.get(z);
            t--;
            map.put(z, t);
            if (!map.containsKey(z >> 1)) {
                map.put(z >> 1, 2);
            } else {
                int t2 = map.get(z >> 1);
                t2 += 2;
                map.put(z >> 1, t2);
            }
            cnt++;
            if ((z >> 1) > 1) {
                ((LinkedList<Integer>) queue).push(z >> 1);
                ((LinkedList<Integer>) queue).push(z >> 1);
            }
        }
        if (cnt < k) {
            System.out.println("NO");
            return;
        }
        System.out.println("YES");
        for (Map.Entry<Integer, Integer> entry :
                map.entrySet()) {
            for (int i = 0; i < entry.getValue(); i++) {
                System.out.print(entry.getKey()+" ");
            }
        }
    }
}