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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"fmt"
)

var m = map[int]map[int]bool{}

func main() {
	var K int
	fmt.Scan(&K)
	var ctr uint64 = 1
	if K%2 == 0 {
		fmt.Println(-1)
		return
	}
	sum := 7
	e := 1
	k := 10 % K
	for {
		if sum%K == 0 {
			fmt.Println(ctr)
			return
		}
		e *= k
		e %= K
		diff := (7 % K) * e
		if v, ok := m[sum%K]; ok {
			if v[diff] {
				fmt.Println(-1)
				return
			}
			m[sum%K][diff%K] = true
		} else {
			m[sum%K] = map[int]bool{diff % K: true}
		}
		sum += diff
		ctr++
	}
}