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.ArrayList;
import java.util.Scanner;

public class PowerOfTwo {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        int k = s.nextInt();
        if(n<k){
            System.out.println("NO");
            return ;
        }
        if(n==k){
            System.out.println("YES");
            for(int i=0;i<n;i++){
                System.out.print(1 + " ");
            }
            return ;
        }
        boolean flag = false;
        if(n%2==1){
            n--;
            k--;
            flag = true;
        }
        ArrayList<Integer> list = new ArrayList<>();
        boolean b = false;
        while(n!=k && n>=0){
            int x = getMax(n);
            while(n-x<k-1)
                x /= 2;
            list.add(x);
            n -= x;
            k--;
            if(n==k && n>=0)
                b = true;
        }
        while(k!=0 && k>0) {
            list.add(1);
            k--;
        }
        if(b){
            System.out.println("YES");
            if(flag)
                System.out.print(1 + " ");
            for(int i=list.size()-1;i>=0;i--)
                System.out.print(list.get(i) + " ");
        }
        else
            System.out.println("NO");
    }
    private static int getMax(int n){
        int i=2;
        while(i<=n)
            i*=2;
        return i/2;
    }
}