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:
import math

n = raw_input().split()
s = int(n[0])
k = int(n[1])

a = [0,1,1]
i = len(a)
while True:
	t = 0
	for j in xrange(1,k+1):
		t += a[i-j]
		if a[i-j] == 0:
			break
	if t > s:
		break
	a.append(t)
	i += 1
#print a
a = list(set(a))
a.sort(reverse=True)

ans = []
for i in a:
	if i <= s:
		s -= i
		ans.append(i)
if s != 0:
	print "you can't"

print len(ans)
for i in ans:
	print i,