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.ArrayDeque;
import java.util.Scanner;

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

        int sum = sc.nextInt();
        int placeHolder = sum;
        int k = sc.nextInt();
        if (sum < k) {
            System.out.println("NO");
            return;
        }
        ArrayDeque<Integer> numbers = new ArrayDeque<>(k);

        for (int i = 0; i < 31; i++) {
            int digit = 1 << i;
            int curr = sum & digit;
            if (curr != 0)
                numbers.add(curr);
        }
        int numberSize = numbers.size();
        if (numberSize > k) {
            System.out.println("NO");
        } else if (numberSize == k) {
            System.out.println("YES");
            printAnswer(numbers);
        } else {
            while (k > numbers.size()) {
                int max = numbers.pollLast();
                int div = max / 2;
                if (div == 1) {
                    numbers.addFirst(div);
                    numbers.addFirst(div);
                } else {
                    numbers.add(max / 2);
                    numbers.add(max / 2);
                }
            }
            int tempSum = numbers.stream().mapToInt(a -> a).sum();
            if (tempSum == placeHolder && numbers.size() == k) {
                System.out.println("YES");
                printAnswer(numbers);
            } else {
                System.out.println("NO");
            }
        }
    }


    public static void printAnswer(ArrayDeque<Integer> numbers) {
        StringBuilder sb = new StringBuilder();
        while (!numbers.isEmpty()) {
            int num = numbers.pop();
            sb.append(num).append(" ");
        }
        System.out.println(sb.toString());
    }
}