Problem:
Score : 700 points

Problem Statement

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Constraints

2 \leq K \leq 10^5

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Sample Input 1

6

Sample Output 1

3

12=6×2 yields the smallest sum.

Sample Input 2

41

Sample Output 2

5

11111=41×271 yields the smallest sum.

Sample Input 3

79992

Sample Output 3

36

Solution in Python (3.4.3) (judge verdict: Accepted)

from collections import deque
K=int(input())

d=[1000000 for x in range(K+1)]
d[1]=0

def bfs(K):
  q=deque()
  q.append(1)
  while q:
    nx=q.popleft()
    if d[(nx*10)%K]>d[nx]:
      d[(nx*10)%K]=d[nx]
      q.appendleft((nx*10)%K)
    if d[(nx+1)%K]>d[nx]+1:
      d[(nx+1)%K]=d[nx]+1
      q.append((nx+1)%K)
  return d[0]+1

print(bfs(K))