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:
def genkbon (s, k):
    if (k<50):
        i = 0
        res = [0]
        while (res[i]<=s):
            if (i<k):
                res.append(0)
            elif (i==k):
                res.append(1)
            elif (i==k+1):
                res.append(1)
            else:
                res.append(2*res[i]-res[i-k])
            i += 1
        del res[-1]
        return res
    if (k>=50):
        res = [0,1]
        i = 1
        while (res[i]<=s):
            res.append(2*res[i])
            i += 1
        return res
    
def solve(s, k, tmp):
    tmp2 = tmp
    while (tmp2[-1]>s):
        del tmp2[-1]
    if (s==0):
        return [0]
    if (s==1):
        return [0,1]
    if (s==2):
        return [0,2]
    ha = tmp2[-1]
    res = solve(s-ha,k,tmp2)
    return [ha]+res
    
inp1 = input()
inp = inp1.split()
hlp = genkbon(int(inp[0]),int(inp[1]))
sol = solve(int(inp[0]),int(inp[1]), hlp)
print(len(sol))
for i in sol[:-1]:
    print(i,end=' ')
print(sol[-1])