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:
n,k = map(int,raw_input().split())

ans = [0]
if k >= 32:
    b = []
    while n > 0:
        b.append(n%2)
        n/=2
    for i in xrange(len(b)):
        if b[i] == 1:
            ans.append(2**i)
else:
    arr = [0 for i in xrange(k-1)]
    arr.append(1)
    ind = 0
    while arr[-1] < n:
        arr.append(sum(arr[ind:k+ind]))
        ind +=1
    ind = len(arr) -1
    while n > 0:
        if arr[ind] <= n:
            n -= arr[ind]
            ans.append(arr[ind])
        ind -= 1

print len(ans)
print " ".join(map(str,ans))