Problem:
Score : 300 points

Problem Statement

Takahashi loves the number 7 and multiples of K.

Where is the first occurrence of a multiple of K in the sequence 7,77,777,\ldots? (Also see Output and Sample Input/Output below.)

If the sequence contains no multiples of K, print -1 instead.

Constraints

1 \leq K \leq 10^6

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print an integer representing the position of the first occurrence of a multiple of K. (For example, if the first occurrence is the fourth element of the sequence, print 4.)

Sample Input 1

101

Sample Output 1

4

None of 7, 77, and 777 is a multiple of 101, but 7777 is.

Sample Input 2

2

Sample Output 2

-1

All elements in the sequence are odd numbers; there are no multiples of 2.

Sample Input 3

999983

Sample Output 3

999982

Solution in PyPy3 (7.3.0) (judge verdict: Accepted)

def main():
    import sys
    import time
    start=time.time()
    K=int(sys.stdin.readline())
    if K%2==0:
        print(-1)
        return

    L=[7%K]
    L2=[7%K]
    if L[0]==0:
        print(1)
        return

    idx=0
    while True:
        L2.append((L2[idx]*10)%K)
        L.append((L[idx]+L2[idx+1])%K)
        if L[-1]==0:
            print(len(L))
            return
        idx+=1

        if time.time()-start>=1.5:
            print(-1)
            return
main()