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: Wrong Answer)

from sys import exit
# A,B,C = [int(n) for n in input().split()]

# a = [int(input()) for _ in range(N)]
# S = str(input())
# L = len(S)
# T = str(input())
# exit()
N = int(input())
K = 10**5
i = 1
ss = set()
while(i != K):
    s = list(str(N*i))
    # print(s)
    tmp = 0
    for j in range(len(s)):
        tmp+=int(s[j])
    # print(tmp)
    ss.add(tmp)
    i+=1
print(sorted(list(ss))[0])