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 A {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        StringBuilder sb = new StringBuilder();

        int n = sc.nextInt();
        int k = sc.nextInt();

        if (n < k) {
            System.out.println("NO");
            return;
        }

        Queue<Integer> queue = new LinkedList<>();

        for (int i = 0; i < 32; i++) {
            if ((n & (1 << i)) > 0) {
                queue.add((1 << i));
            }
        }

        if (queue.size() > k) {
            System.out.println("NO");
            return;
        }

        while (queue.size() < k) {

            int cur = queue.remove();

            if (cur == 1) {
                queue.add(1);
            }

            int half = cur / 2;

            if (half > 0) {
                queue.add(half);
                queue.add(half);
            }

        }

        if (queue.size() < k) {
            System.out.println("NO");
            return;
        }

        sb.append("YES").append("\n");

        while (!queue.isEmpty()) {
            sb.append(queue.remove()).append(" ");
        }

        sb.append("\n");

        System.out.print(sb);
    }
}