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 PYTHON):

Solution:
# -*- coding: utf-8 -*-

from __future__ import absolute_import
from __future__ import division
from __future__ import generators
from __future__ import nested_scopes
from __future__ import print_function
from __future__ import unicode_literals
from __future__ import with_statement

import bisect
import collections
import copy
import functools
import heapq
import itertools
import math
import operator
import os
import re
import random
import sys
from pprint import pprint

__author__ = 'Aphrodite'


def main():
    iterator = itertools.imap(str.rstrip, sys.stdin.readlines())
    s, k = map(int, next(iterator).split())
    a = [0, 1]
    while a[-1] < s:
        if (len(a)) < k:
            a.append(sum(a))
        else:
            a.append(sum(a[-k:]))
#    print(a)
    res = []
    while s > 0:
        idx = bisect.bisect(a, s) - 1
        s -= a[idx]
        res.append(a[idx])
    if len(res) == 1:
        res.append(0)
    print(len(res))
    print(' '.join(map(str, res)))


if __name__ == '__main__':
    main()