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.io.ByteArrayInputStream;
import java.util.Scanner;

public class Pow2 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
//        Scanner sc = testdata();
        int n = sc.nextInt();
        int k = sc.nextInt();
        if (k > n) {
            System.out.println("NO");
            return;
        }
        int[] arr = new int[100];
        int i = 0;
        int sum1 = 0;

        while (n > 0) {
            arr[i] = (n % 2);
            if (arr[i] == 1) {
                sum1++;
            }
            n /= 2;
            i++;
        }
        if (k < sum1) {
            System.out.println("NO");
            return;
        }

        while (sum1 != k) {
            int diff = Math.min(k-sum1, arr[i]);
            arr[i-1] += (diff*2);
            arr[i] -= diff;
            sum1 += diff;
            i--;
        }

        System.out.println("YES");
        boolean first = true;
        int currPow = 1;
        for (int j = 0; j < 100; j++) {
            for (int x = 0; x < arr[j]; x++) {
                if (first) {
                    System.out.print(currPow);
                    first = false;
                } else {
                    System.out.print(" "+currPow);
                }
            }
            currPow *= 2;
        }
        System.out.println();
    }
    static Scanner testdata() {
        return new Scanner(new ByteArrayInputStream((
                "1000000000 15"
        ).getBytes()));
    }
}