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=[0,1]
ss=1
tpos=1
tpos_d=-k+2
while f[-1]<s:
    f.append(ss)
    ss=ss+ss
    if tpos_d>=0:
        ss-=f[tpos_d]
    tpos+=1
    tpos_d+=1
rere=[0]
x=1
while s>0:
    while f[-x]>s:
        x+=1
    s-=f[-x]
    rere.append(f[-x])
print len(rere)
print " ".join(map(str,rere))