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.Scanner;

/**
 *
 * @author acm
 */
public class JavaApplication1 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        
		long dp[] = new long[101];
		Scanner in = new Scanner(System.in);
		int s,k;		
		s = in.nextInt();
		k = in.nextInt();
                
		dp[0] = 1;
                
                
		int counter = 0;
		for(int i = 1;; i++)
		{
			int prev = i - k;

			if(prev < 0 )
                            prev = 0;
                        
			for(int j = prev; j <= i-1 ;j++)
			{
				dp[i] += dp[j];
			}

			if( dp[i] > (long) s )
                            break;
                        
			counter++;
		}
                
		int sol[] = new int[101];
		int nums = 0;
                
		for(int i = counter; i >= 0; i--)
		{
			if( s >= dp[i] ){
                            
				s -= dp[i];
				sol[nums] = (int) dp[i];
                                nums++;
                                
			}
		}
                
		sol[nums] = 0;
                nums++;
                
		System.out.println(nums);
                
		for(int i=0;i<nums;i++)
                    System.out.print(sol[i] +" ");
                
	}

}