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
import java.util.Scanner;


public class WellKnownNumbers {
	public static void main(String args[]){
		Scanner in = new Scanner(System.in);
		int s=in.nextInt();
		int k=in.nextInt();
		
		int a[]=new int[1000000];
		int c =1;
		int sc=1;
		a[1]=1;
		int sum = 0;
		while(a[c]<=s){
			if(c>k) sum -=a[sc++];
			sum+=a[c++];
			a[c]= sum;
			
			
		}
		
		c--;
		String ss="";
		int count=0;
		while(s>0){
			if(s>=a[c]){
				s-=a[c];
				count++;
				ss= a[c]+ " "+ ss;
			}
			c--;
		}
		if(count==1){
			System.out.println(2);
			System.out.println(ss+"0");
		}
		else{
			System.out.println(count);
			System.out.println(ss);
		}
	}
}