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 sys
if sys.version_info[0] == 2: input = raw_input
s, k = map(int,input().split())
if s == 1:
    print('2\n0 1')
    sys.exit(0)
elif s==2:
    print('2\n0 2')
    sys.exit(0)
n = 2
ans = []
a = [0] * 100
a[0] = a[1] = 1
while a[n-1] < s:
    a[n] = 2*a[n-1]-(a[n-k-1] if n-k-1>=0 else 0)
    n += 1

for i in range(n-1,-1,-1):
    if a[i] <= s:
        ans.append(a[i])
        s -= a[i]
        if s == 0: break
print(len(ans) + 1)
print('0 ' + " ".join(map(str,ans)))