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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define ll long long
#define LL long long
#define db double
#define iosks std::ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
using namespace std;
#define PI acos(-1)
ll mod=1e9+7;
ll ksm(ll n,ll k)
{
    ll ans=1;
    while(k)
    {
        if(k&1)
            ans=(ans*n)%mod;
        k>>=1;
        n=(n*n)%mod;
    }
    return ans;
}
ll prime(ll n)
{
    ll sq=sqrt(n);
    for(int i=2;i<=sq;i++)
    {
        if(n%i==0)
            return false;
    }
    return true;
}
int main()
{
    ll n;
    cin >> n;
    ll t=7,ct=1;
    ll inv=ksm(9,mod-2);
    ll ninv=ksm(n,mod-2);
    while(t<n)
    {
        t=t*10+7;
        ct++;
    }
    for(int i=ct;i<=n;i++)
    {
        ll tn=((ksm(10,i)+mod-1)*7%mod)*inv%mod;

        if(tn*ksm(tn*inv%mod,mod-2)%mod==n%mod)
        {
            cout << i;
            return 0;
        }
    }
    cout << -1;
    return 0;
}