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 PYTHON):

Solution:
s,k = map(int,raw_input().split());

A = [0,1];
su = 0;
l = 1;
for i in xrange(k-1):
	su += l;
	l = su;
	A.append(l);
	if su >= s: break;

su += l;
q = A;
i = 1;
while A[-1] < s:
	A.append(su);
	su -= A[i];
	su += A[-1];
	i += 1;

B = [];
while s :
	while A[-1] > s: A.pop();
	s -= A[-1];
	B.append(A[-1]);

if len(B) < 2:
	B.append(0);
print len(B);
print " ".join([str(b) for b in B]);