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:
// package Practice2.CF225;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.TreeMap;

public class CF225B {
    public static void main(String[] args) throws IOException {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        String[] ns = bf.readLine().split(" ");
        int s = Integer.parseInt(ns[0]), k = Integer.parseInt(ns[1]);
        TreeMap<Integer, Long> memo = new TreeMap<Integer, Long>();
        long sum = 0;
        int i = 0;
        for(i = k;sum<=s;i++){
            long kbon = 0;
            if(i==k)
                kbon = 1;
            else
                kbon = sum;
            memo.put(i, kbon);
            sum += kbon;
            if(i-k>=k)
                sum -= memo.get(i-k);
        }
        //System.out.println(memo.toString());
//		for(i = i; i>=k;i--){
//			long target = s-memo.get(i);
//			long attempt = 0;
//			int high = i-1, low = k, mid = 0;
//			while(high>=low){
//				mid = (high+low)/2;
//				attempt = memo.get(mid);
//				if(attempt>target)
//					high = mid-1;
//				else if(attempt<target)
//					low = mid+1;
//				else
//
//			}
//		}
        long target = s;
        StringBuilder sb = new StringBuilder();
        i--;
        int c = 0;
        for(i = i;target>0;i--){
            //System.out.println(i);
            long curr = memo.get(i);
            if(target-curr>=0){
                c++;
                target -= curr;
                sb.append(""+curr+" ");
            }
        }
        if(c==1){
            c++;
            sb.append("0");
        }
        System.out.println(c);
        System.out.println(sb.toString());
    }
}