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:
s,k=map(int,raw_input().split())
f,sm=[0,1,1],[0]
ssum=0
while ssum<s :
    i=k+2
    sumi=1
    while sumi<=s-ssum :
        sumi+=f[i-k]
        i+=1
        if ssum==0 :
            f.append(2*f[i-k-1])
            if i-k-k-1 >=0 :
                f[i-k]=f[i-k]-f[i-k-k-1]
    ssum+=f[i-k-1]
    sm.append(f[i-k-1])
print(len(sm))
print(" ".join([str(i) for i in sm]))