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.*;

public class PowersofTwo105C {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        if(n<k) {
            System.out.println("NO");
            return;
        }
        List<Integer> lis = getArrayList(n);
        if(lis.size() > k) {
            System.out.println("NO");
            return;
        }
        List<Integer> res = new ArrayList<>();
//        Collections.sort(lis);
//        Collections.reverse(lis);
//        int i = 0;
//        while((res.size() + lis.size()-i) != k) {
//            int temp = lis.get(i);
//            while((res.size() + lis.size()-i) != k) {
//                res.add(temp/2);
//                res.add(temp/2);
//            }
//        }
        Queue<Integer> queue =  new LinkedList<>();
        Queue<Integer> queue2 = new LinkedList<>();
        for(int i: lis) {
            queue.add(i);
        }
        while(queue.size() < k) {
            while(queue2.size() + queue.size() < k && queue.size() != 0) {
                int temp = queue.remove();
                if(temp != 1) {
                    queue2.add(temp/2);
                    queue2.add(temp/2);
                } else {
                    queue2.add(temp);
                }
            }
            while(queue2.size() != 0) {
                queue.add(queue2.remove());
            }
        }
        while(queue.size() > 0) {
            res.add(queue.remove());
        }
        System.out.println("YES");
        Collections.sort(res);
        for(int i: res) {
            System.out.print(i + " ");
        }
        System.out.println();
    }
    static List<Integer> getArrayList(int n) {
        int cur = 1;
        List<Integer> arr = new ArrayList<>();

        while(n > 0) {
            if(n%2 == 1) {
                arr.add(cur);
            }
            n = n/2;
            cur = cur*2;
        }
        return arr;

    }

}