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:
x,y=map(int,input().split())
dp=[]
dp.append(0)
dp.append(1)

n=2
while 1:
    sm=0
    for k in range(n-1,n-y-1,-1):
        if k==0:
            break
        sm+=dp[k]
    if sm>x:
        break
    dp.append(sm)
    n+=1

dp.reverse()
res=[]

n=0
while n<len(dp) and x>=0:
    if x>=dp[n]:
        res.append(dp[n])
        x-=dp[n]
    n+=1

print(len(res))
print(*res)