Well-known Numbers

2000ms

262144K

Description:

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, ..., a_m. 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.

Sample Input:

5 2

Sample Output:

3
0 2 3

Sample Input:

21 5

Sample Output:

3
4 1 16

Informação

Provedor Codeforces

Código CF225B