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.Scanner;

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

        int total = sc.nextInt();
        int size = sc.nextInt();
        int[] arr = new int[size];
        int index = 0, temp;
        while (total != 0 && index < size) {
            temp = Integer.highestOneBit(total);
            arr[index++] = temp;
            total -= temp;
            if (index > size) {
                System.out.println("NO");
                return;
            }
        }
        if (total == 0 && index == size) {
            System.out.println("YES");
            for (int i = 0; i < size; i++) {
                System.out.print(arr[i] + " ");
            }
            return;
        } else if (index < size) {
            int tempIndex = 0;
            while (index != size) {
                if (arr[tempIndex] == 1) {
                    tempIndex++;
                    continue;
                } else if (arr[tempIndex] == 0) {
                    System.out.println("NO");
                    return;
                }
                arr[tempIndex] /= 2;
                arr[index] = arr[tempIndex];
                index++;
            }
            System.out.println("YES");
            for (int i = 0; i < size; i++) {
                System.out.print(arr[i] + " ");
            }
            return;
        } else {
            System.out.println("NO");
            return;
        }

    }
}