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 PYTHON3):

Solution:
s,k=[int(i) for i in input().split()]
a=[-1,0,1,1]
i=3
while a[i]<=pow(10,9):
    i+=1
    a.append(0)
    if i<=k:
        for j in range(1,i):
            a[i]+=a[j]
    else:
        for j in range(i-k,i):
            a[i]+=a[j]
b=[]
for j in range(i,0,-1):
    if a[j]<=s:
        b.append(a[j])
        s-=a[j]
        if s==0:
            b.append(0)
            break
print(len(b))
for i in b:
    print(i,end=' ')