Problem: Numbers k-bonacci (k is integer, k > 1) are a generalization of Fibonacci numbers and are determined as follows:

  * F(k, n) = 0, for integer n, 1 ≤ n < k; 
  * F(k, k) = 1; 
  * F(k, n) = F(k, n - 1) + F(k, n - 2) + ... + F(k, n - k), for integer n, n > k. 



Note that we determine the k-bonacci numbers, F(k, n), only for integer values of n and k.

You've got a number s, represent it as a sum of several (at least two) distinct k-bonacci numbers. 

Input

The first line contains two integers s and k (1 ≤ s, k ≤ 109; k > 1).

Output

In the first line print an integer m (m ≥ 2) that shows how many numbers are in the found representation. In the second line print m distinct integers a1, a2, ..., am. Each printed integer should be a k-bonacci number. The sum of printed integers must equal s.

It is guaranteed that the answer exists. If there are several possible answers, print any of them.

Examples

Input

5 2


Output

3
0 2 3


Input

21 5


Output

3
4 1 16

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.lang.*;
public class B_Well_known_Numbers{
static Scanner sc=new Scanner(System.in);
public static void main(String[] args){
    int s=sc.nextInt();
    int k=sc.nextInt();
    int arr[]=new int[1000000];
    int i=1,index=-1;
    arr[1]=1;
    // System.out.println();
    while(true){
        // System.out.print(arr[i]+" ");
        if(arr[i]>=s){
            index=i;
            break;
        }
        i++;
        for(int j=Math.max(1,i-k);j<i;j++){
            arr[i]+=arr[j];
        }
    }
    ArrayList<Integer> a=new ArrayList<>();
    a.add(0);
    for(i=index;i>=1;i--){
        if(s>=arr[i]){
            s=s-arr[i];
            a.add(arr[i]);
        }
        if(s==0){
            break;
        }
    }
    System.out.println(a.size());
    for(int u:a){
        System.out.print(u+" ");
    }
    
}
}