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B. Well-known Numbers
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 ≤ 109k > 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