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())
t={}
def f(a,b):
    s=0
    if b < a:  s=0
    elif b == a: s=1
    elif b in t:
        s=t[b]
    elif a > 32: s=2**(b-a-1)
    else:
        for i in range(b-a,b):
            s+=f(a,i)
    t[b] = s
    return s

i=max(0,k-2)
e=0
F=[]
while e < s:
    i+=1
    e=f(k,i)
    if e < s or 0 in F:
        F+=[e]
   
r=[]
for e in reversed(F):
    if e <= s and e:
        r+=[`e`]
        s-=e
if len(r)==1 and 0 in F:
    r+=['0']
print len(r)
print ' '.join(r)