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
#
#sys.stdin = open('in.txt', 'r')

s, k = map(int, raw_input().split())
fib = [0, 1, 1]

while(True):
    fib.append(sum(fib[-k:]))
    if fib[-1] > s: 
        del fib[-1]
        break

ans = []

while(True):
    x = fib.pop()
    if x <= s: 
        s -= x
        ans.append(x)
    if s == 0:
        break
ans.append(0)
print len(ans)
print ' '.join(map(str, ans))