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=list(map(int,input().split(' ')))
a=[0,1,1]
while a[-1]<s:
    if len(a)<k:
        a.append(sum(a))
    else:
        t=0
        for i in range(k):
            t+=a[-i-1]
        a.append(t)
if s==a[-1]:
    print(2)
    print(0,a[-1])
else:
    use=[]
    for i in range(len(a)):
        if s>=a[-i-1]:
            s-=a[-i-1]
            use.append(a[-i-1])
    print(len(use))
    for i in use:
        print(i,end=' ')