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.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class Code {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int k = scanner.nextInt();
        int m = n;
        int ct = 0;
        int num = 1;
        TreeMap<Integer, Integer> map = new TreeMap<>();
        while (m != 0) {
            if ((m & 1) == 1) {
                map.put(num, 1);
                ++ct;
            }
            m >>= 1;
            num <<= 1;
        }
        if (k >= ct && k <= n) {
            System.out.println("YES");
            while (ct != k) {
                int max = map.lastKey();
                int maxCt = map.get(max);
                map.putIfAbsent(max / 2, 0);
                map.computeIfPresent(max / 2, (key, value) -> value + 2);
                if (maxCt == 1) {
                    map.remove(max);
                } else {
                    map.computeIfPresent(max, (key, value) -> value - 1);
                }
                ++ct;
            }
            for (Map.Entry<Integer, Integer> entry : map.entrySet()) {
                for (int i = 0; i < entry.getValue(); i++) {
                    System.out.print(entry.getKey());
                    System.out.print(" ");
                }
            }
        } else {
            System.out.println("NO");
        }
    }
}