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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class P3 {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;

        st = new StringTokenizer(in.readLine());

        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());

        if(k > n){
            System.out.println("NO");
        }
        else{
            int a[] = new int[1000000];
            int len = 0;
            while(k != n && k!=0){
                int diff = n-(k-1);
                int logVal = (int)(Math.log(diff)/Math.log(2));
                a[len++] = 1<<logVal;
                n -= (1<<logVal);
                k--;
            }
            while(k > 0){
                a[len++] = 1;
                k--;
                n--;
            }
            if(n != 0){
                System.out.println("NO");
            }
            else{
                System.out.println("YES");
                for(int i = 0; i < len; i++){
                    System.out.print(a[i]+" ");
                }
                System.out.println();
            }

        }
    }
}