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:
NAME = "P2"
try:
    inFile = open(NAME+".txt")
except:
    pass

def read():
    try:
        return inFile.readline().strip()
    except:
        return raw_input().strip()

s,k = map(int,read().split())
seq = [1,1]
n = 2
x = 1

while seq[-1] < s:
    x *= 2
    if n > k:
        x -= seq[n-k-1]
    seq.append(x)
    n += 1
#print seq

ans = []
i = len(seq)-1
while s > 0:
    while seq[i] > s:
        i -= 1
    ans.append(seq[i])
    s -= seq[i]
if len(ans) == 1:
    ans.append(0)
    
print len(ans)
print " ".join(map(str,ans))