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 io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def binarySearch(arr,l,r,val):
    while l<=r:
        mid=(l+r)//2
        if arr[mid]==val:
            ans=mid
            break
        elif arr[mid]<val:
            ans=mid
            l=mid+1
        else:
            r=mid-1
    return ans
def fib(k,s):
    arr=[]
    i=1
    temp=True
    l=0
    while temp:
        if k>i:
            arr.append(0)
            l+=1
            if arr[-1]>s:
                arr.pop()
                l-=1
                break
            i=k
        elif k==i:
            arr.append(1)
            l+=1
            if arr[-1]>s:
                arr.pop()
                l-=1
                break
            i+=1
        else:
            if l<=k:
                num=sum(arr)
                arr.append(num)
                l+=1
                if arr[-1]>s:
                    arr.pop()
                    l-=1
                    break
            else:
                num+=arr[-1]
                num-=arr[-k-1]
                arr.append(num)
                l+=1
                if arr[-1]>s:
                    arr.pop()
                    l-=1
                    break
            i+=1
    return arr
s,k=list(map(int,input().split())) 
arr=fib(k,s)
l=len(arr)-1
ans=arr[l]
lis=[ans]
while ans<s:
    temp=s-ans
    ind=binarySearch(arr,0,l,temp)
    ans+=arr[ind]
    lis.append(arr[ind])
answer=[]
a=len(lis)
if a==1:
    lis.append(0)
    a+=1
for i in range(1,a+1):
    answer.append(lis[-i])
print(a)
print(" ".join(str(x) for x in answer))