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: Accepted)

#include <bits/stdc++.h>
#define REP(i, n) for(int i = 0;i < n;i++)
#define ll long long
using namespace std;
typedef pair<int, int> P;
typedef pair<ll,ll> LP;
const int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
const int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
const int INF = 1000000000;
const ll LINF = 1000000000000000000;//1e18
const ll MOD = 1000000007;
const ll MOD2 = 998244353;
const double PI = acos(-1.0);
const double EPS = 1e-10;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
//template<class T> inline void add(T &a, T b){a = ((a+b) % MOD + MOD) % MOD;};

/*  ----------------------- DEBUG FUNCTION ---------------------------- */
void debug(){ cerr << "\n"; }
template <class Head, class... Tail>
void debug(Head && head, Tail &&... tail){
    cerr << head;
    if(sizeof...(Tail) > 0){
        cerr << ", ";
    }
    debug(std::move(tail)...);
}
// pair
template <typename T, typename U>
void debug(pair<T, U> &p){
    cerr << "(" << p.first << ", " << p.second << ")";
}
// vector
template <typename T>
void debug(vector<T> &vec){
    cerr << "{";
    for(int i=0;i<vec.size();i++){
        cerr << vec[i] << (i + 1 == vec.size() ? "" : ", ");
    }
    cerr << "}\n";
}
// map
template <typename T, typename U>
void debug(map<T, U> &mp){
    cerr << "{";
    for(auto itr=mp.begin();itr!=mp.end();itr++){
        debug(*itr);
        itr++;
        if(itr != mp.end()) cerr << ", ";
        itr--;
    }
    cerr << "}\n";
}
// set
template <typename T>
void debug(set<T> &st){
    cerr << "{";
    for(auto itr=st.begin();itr!=st.end();itr++){
        debug(*itr);
        itr++;
        if(itr != st.end()) cerr << ", ";
        itr--;
    }
    cerr << "}";
}
/*  ----------------------- DEBUG FUNCTION ---------------------------- */

template<int MOD> struct Fp {
    long long val;
    constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    constexpr int getmod() { return MOD; }
    constexpr Fp operator - () const noexcept {
        return val ? MOD - val : 0;
    }
    constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp& r) noexcept {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp& r) noexcept {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp& r) noexcept {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr bool operator == (const Fp& r) const noexcept {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp& r) const noexcept {
        return this->val != r.val;
    }
    friend constexpr ostream& operator << (ostream &os, const Fp<MOD>& x) noexcept {
        return os << x.val;
    }
    friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(a, n / 2);
        t = t * t;
        if (n & 1) t = t * a;
        return t;
    }
};

template<class T> struct BiCoef {
    vector<T> fact_, inv_, finv_;
    constexpr BiCoef() {}
    constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
        init(n);
    }
    constexpr void init(int n) noexcept {
        fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
        int MOD = fact_[0].getmod();
        for(int i = 2; i < n; i++){
            fact_[i] = fact_[i-1] * i;
            inv_[i] = -inv_[MOD%i] * (MOD/i);
            finv_[i] = finv_[i-1] * inv_[i];
        }
    }
    constexpr T com(int n, int k) const noexcept {
        if (n < k || n < 0 || k < 0) return 0;
        return fact_[n] * finv_[k] * finv_[n-k];
    }
    constexpr T fact(int n) const noexcept {
        if (n < 0) return 0;
        return fact_[n];
    }
    constexpr T inv(int n) const noexcept {
        if (n < 0) return 0;
        return inv_[n];
    }
    constexpr T finv(int n) const noexcept {
        if (n < 0) return 0;
        return finv_[n];
    }
    constexpr T perm(int n, int k) const noexcept {
        if (n < k || n < 0 || k < 0) return 0;
        return fact_[n] * finv_[n-k];
    }
};

using mint = Fp<MOD>;
BiCoef<mint> bc;
// using vec = vector<mint>;
// using mat = vector<vec>;

void solve(){
    int K;
    cin >> K;

    int cur = 0;
    REP(i,K+1){
        cur = cur * 10 + 7;
        cur %= K;
        if(cur == 0){
            cout << i + 1 << endl;
            return;
        }
    }
    cout << -1 << endl;
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    solve();
    // int T; cin >> T; REP(t,T) solve();
}