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:
import math,sys
#from itertools import permutations, combinations;import heapq,random;
from collections import defaultdict,deque
import bisect as bi
def yes():print('YES')
def no():print('NO')
#sys.stdin=open('input.txt','r');sys.stdout=open('output.txt','w');
def I():return (int(sys.stdin.readline()))
def In():return(map(int,sys.stdin.readline().split()))
def Sn():return sys.stdin.readline().strip()
#sys.setrecursionlimit(1500)
def dict(a):
    d={} 
    for x in a:
        if d.get(x,-1)!=-1:
            d[x]+=1
        else:
            d[x]=1
    return d
def find_gt(a, x):
    'Find leftmost value greater than x'
    i = bi.bisect_left(a, x)
    if i != len(a):
        return i
    else:            
        return -1
  
def main():
    try:
        s,n=In()
        
        if n<=32:
            l=[0]*(n+1)
            l[n]=1
            for i in range(n+1,n+60):
                total=0
                for j in range(i-n,i):
                    total+=l[j]
                l.append(total)
            ans=[]
            j=len(l)-1
            while s>0:
                if l[j]<=s and l[j]!=0:
                    ans.append(l[j])
                    s-=l[j]
                j-=1
            if len(ans)==1:
                ans.append(0)

            print(len(ans))
            print(*ans)
        else:
            ans=[]
            j=30
            while s:
                t=pow(2,j)
                if t<=s:
                    ans.append(t)
                    s%=t
                j-=1
            if len(ans)==1:
                ans.append(0)

            print(len(ans))
            print(*ans)

    except:
        pass
        
M = 998244353
P = 1000000007
 
if __name__ == '__main__':
    # for _ in range(I()):main()
    for _ in range(1):main()
#End#

#        ******************* All The Best *******************   #