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.ArrayList;
import java.util.HashSet;
import java.util.Scanner;

public class Round139_B {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);

		int s = in.nextInt();
		int k = in.nextInt();
		int MAX = 50;
		long[] a = new long[MAX];
		int maxl = Math.min(MAX, k);
		a[0] = 1;
		long sum = 1;
		boolean done = true;
		int lasto = 0;
		for (int i = 1; i < maxl; i++) {
			a[i] = sum;
			sum += sum;
			if (done && a[i] < 1000000100)
				lasto = i;
			else
				done = false;
		}

		for (int i = maxl; i < MAX; i++) {
			a[i] = 2 * a[i - 1] - (((i - (k + 1)) > -1) ? a[i - (k + 1)] : 0);
			if (done && a[i] < 1000000100)
				lasto = i;
			else
				done = false;
		}

		StringBuffer ans = new StringBuffer("");
		int tmp = s;
		int count = lasto;
		ArrayList<Long> fin = null;
		
		while (count > -1) {
			fin = new ArrayList<Long>();
			HashSet<Integer> hash = new HashSet<Integer>();
			tmp = s;
			for (int j = count; j > -1; j--) {
				if (a[j] <= tmp) {
					
					if (hash.contains((int) a[j]))
						continue;
					tmp -= a[j];
					fin.add(a[j]);
					hash.add((int) a[j]);
				}
			}
			if (tmp == 0)
				break;
			count--;
		}
		if (fin.size() == 1)
			fin.add((long)0);
		int m = fin.size();
		System.out.println(m);
		if (m != 0)
			ans.append(fin.get(0));
		for (int i = 1; i < m; i++)
			ans.append(" " + fin.get(i));
		System.out.println(ans.toString());
	}
}