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 Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        StringBuilder stringBuilder = new StringBuilder();
        // x = 2^z
        int[] pows = new int[64];
        long n = scanner.nextInt();
        long k = scanner.nextInt();
        int current = 0;
        for (int i = 0; i < 32; ++i) {
            if ((n & (1 << i)) != 0) {
                current++;
                pows[i]++;
            }
        }
        if (current > k) {
            System.out.println("NO");
        } else {
            while (current != k) {
                boolean re = true;
                for (int i = 33; i >= 1; --i) {
                    if (pows[i] > 0) {
                        pows[i - 1] += 2;
                        pows[i]--;
                        current++;
                        re = false;
                        break;
                    }
                }
                if (re) break;
            }
            if (current == k) {
                System.out.println("YES");
                for (int i = 33; i >= 0; --i) {
                    for (int j = 0; j < pows[i]; ++j) stringBuilder.append(1 << (1L * i)).append(' ');
                }
                System.out.println(stringBuilder);
            } else {
                System.out.println("NO");
            }
        }
    }
}