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 bisect
s,k=map(int,raw_input().split())
if k>31:
    a=[0,1,2]
    while a[-1] < s:a.append(a[-1]*2)
else:
    a=[0]*(k-1)+[1]
    while a[-1] < s:a.append(sum(a[-k:]))
curr = bisect.bisect_left(a, s)
ans=[]
while s:
    curr = bisect.bisect_left(a, s)
    if a[curr] > s:curr-=1
    ans.append(a[curr])
    s-=a[curr]
ans+=[0]
print len(ans)
print " ".join(map(str,ans))