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.Arrays;
import java.util.Scanner;

public class PowersOfTwo {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int k = scanner.nextInt();
        if (k > n) {
            System.out.println("NO");
            return;
        }
        int[] a = new int[33];

        for (int i = 0; i < 32; i++) {
            if ((n & (1 << i)) > 0) {
                a[i]++;
                k--;
            }
        }

        if (k < 0) {
            System.out.println("NO");
            return;
        }
//        System.out.println(Arrays.toString(a));

        System.out.println("YES");
        for(int i = 32; i > 0; i--) {
            int minus = Math.min(a[i], k);
            a[i - 1] += minus * 2;
            a[i] -= minus;
            k -= minus;
        }

        for (int i = 0; i < 32; i++) {
            while(a[i] > 0) {
                System.out.print((1 << i) + " ");
                a[i]--;
            }
        }
    }
}