結果

問題 No.3028 No.9999
ユーザー 横山緑
提出日時 2025-02-21 21:50:36
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 4,000 ms
コード長 9,014 bytes
コンパイル時間 4,007 ms
コンパイル使用メモリ 293,692 KB
実行使用メモリ 6,824 KB
最終ジャッジ日時 2025-02-21 21:50:43
合計ジャッジ時間 4,972 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 23
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#line 2 "template.hpp"
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
// https://xn--kst.jp/blog/2019/08/29/cpp-comp/
// debug methods
// usage: debug(x,y);
// vector 出力できるように修正
template <typename T>
ostream& debug_print(ostream& os, const vector<T>& v) {
    os << "[";
    for (size_t i = 0; i < v.size(); ++i) {
        os << v[i];
        if (i < v.size() - 1) os << ", ";
    }
    os << "]";
    return os;
}
template <typename T>
ostream& debug_print(ostream& os, const T& var) {
    os << var;
    return os;
}
#define CHOOSE(a) CHOOSE2 a
#define CHOOSE2(a0, a1, a2, a3, a4, x, ...) x
#define debug_1(x1) { cout << #x1 << ": "; debug_print(cout, x1) << endl; }
#define debug_2(x1, x2) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << endl; }
#define debug_3(x1, x2, x3) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << ", " << #x3 << ": "; 
    debug_print(cout, x3) << endl; }
#define debug_4(x1, x2, x3, x4) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << ", " << #x3 << ": "; 
    debug_print(cout, x3) << ", " << #x4 << ": "; debug_print(cout, x4) << endl; }
#define debug_5(x1, x2, x3, x4, x5) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << ", " << #x3 << ": "
    ; debug_print(cout, x3) << ", " << #x4 << ": "; debug_print(cout, x4) << ", " << #x5 << ": "; debug_print(cout, x5) << endl; }
#ifdef LOCAL
#define debug(...) CHOOSE((__VA_ARGS__, debug_5, debug_4, debug_3, debug_2, debug_1, ~))(__VA_ARGS__)
#else
#define debug(...)
#endif
using ll = long long;
using vl = vector<ll>;
using Graph = vector<vector<ll>>;
using P = pair<ll, ll>;
#define all(v) v.begin(), v.end()
template <typename T> inline bool chmax(T &a, T b) {
    return ((a < b) ? (a = b, true) : (false));
}
template <typename T> inline bool chmin(T &a, T b) {
    return ((a > b) ? (a = b, true) : (false));
}
#define rep1(i, n) for(ll i = 1; i <= ((ll)n); ++i)
// https://trap.jp/post/1224/
template <class... T> constexpr auto min(T... a) {
    return min(initializer_list<common_type_t<T...>>{a...});
}
template <class... T> constexpr auto max(T... a) {
    return max(initializer_list<common_type_t<T...>>{a...});
}
template <class... T> void input(T &...a) { (cin >> ... >> a); }
template <class T> void input(vector<T> &a) {
    for(T &x : a)
        cin >> x;
}
void print() { cout << '\n'; }
template <class T, class... Ts> void print(const T &a, const Ts &...b) {
    cout << a;
    (cout << ... << (cout << ' ', b));
    cout << '\n';
}
void print(const string &s) {
    cout << s << '\n';
}
template <class Container, typename = void>
struct is_container : std::false_type {};
template <class Container>
struct is_container<Container, std::void_t<decltype(std::declval<Container>().begin()), decltype(std::declval<Container>().end())>> : std::true_type 
    {};
template <class Container>
typename enable_if<is_container<Container>::value>::type print(const Container& x) {
    if (!x.empty()) {
        auto it = x.begin();
        for (; it != prev(x.end()); ++it) {
            cout << *it << " ";
        }
        cout << *it << "\n";  // 最後の要素を出力して改行
    }
}
#define INT(...)                                                               \
    int __VA_ARGS__;                                                           \
    input(__VA_ARGS__)
#define LL(...)                                                                \
    long long __VA_ARGS__;                                                     \
    input(__VA_ARGS__)
#define STR(...)                                                               \
    string __VA_ARGS__;                                                        \
    input(__VA_ARGS__)
#define REP1(a) for(ll i = 0; i < a; i++)
#define REP2(i, a) for(ll i = 0; i < a; i++)
#define REP3(i, a, b) for(ll i = a; i < b; i++)
#define REP4(i, a, b, c) for(ll i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
ll inf = 3e18;
vl dx = {1, -1, 0, 0};
vl dy = {0, 0, 1, -1};
#line 3 "math/mod-pow.hpp"
int mod_pow(int x, ll n, int mod) {
    assert(n >= 0);
    ll res = 1, xpow = x;
    while(n) {
        if(n & 1) {
            res = res * xpow % mod;
        }
        xpow = xpow * xpow % mod;
        n >>= 1;
    }
    return res;
}
ll mod_pow_ll(ll x, ll n, ll mod) {
    assert(n >= 0);
    __int128 res = 1, xpow = x;
    while(n) {
        if(n & 1) {
            res = res * xpow % mod;
        }
        xpow = xpow * xpow % mod;
        n >>= 1;
    }
    return res;
}
#line 4 "math/miller_rabin.hpp"
// https://drken1215.hatenablog.com/entry/2023/05/23/233000
// todo モンゴメリ乗算
bool is_prime(ll n) {
    if(n == 2 or n == 7 or n == 61) {
        return true;
    }
    if(n % 2 == 0 or n == 1) {
        return false;
    }
    ll d = n - 1;
    ll s = 0;
    while(d % 2 == 0) {
        d >>= 1;
        s++;
    }
    auto check = [&](ll a) {
        ll ad = mod_pow_ll(a, d, n);
        if(ad == 1) {
            return true;
        }
        rep(i, s) {
            if(ad == n - 1) {
                return true;
            }
            if(i < s - 1)
                ad = mod_pow_ll(ad, 2, n);
        }
        return false;
    };
    if(n < 4759123141) {
        for(auto a : vl{2, 7, 61}) {
            if(!check(a)) {
                return false;
            }
        }
        return true;
    } else {
        for(auto a : vl{2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
            if(n == a) {
                return true;
            }
            if(!check(a)) {
                return false;
            }
        }
        return true;
    }
}
#line 3 "math/pollard_rho.hpp"
// https://manabitimes.jp/math/1192
// https://wacchoz.hatenablog.com/entry/2019/01/05/230128
// https://nyaannyaan.github.io/library/prime/fast-factorize.hpp
namespace fast_factorize {
ll pollard_rho(ll n) {
    // nの素因数を１つ返す
    // 1には1を返す
    if(n == 1) {
        return 1;
    }
    if(~n & 1) {
        return 2;
    }
    if(is_prime(n)) {
        return n;
    }
    ll r = 1;
    auto f = [&n, &r](ll m) { return ((__int128)m * m + r) % n; };
    ll x = 1, y = f(x);
    while(1) {
        ll g = gcd(n, abs(x - y));
        if(1 < g and g < n) {
            return pollard_rho(g);
        } else if(g == 1) {
            x = f(x);
            y = f(f(y));
        } else {
            r = rand() % (n - 2) + 2;
            x = 1;
            y = f(x);
        }
    }
}
vl inner_factorize(ll n) {
    vl res;
    if(n == 1) {
        return res;
    }
    while(n > 1 and !is_prime(n)) {
        ll p = pollard_rho(n);
        while(n % p == 0) {
            res.push_back(p);
            n /= p;
        }
    }
    if(n > 1) {
        res.push_back(n);
    }
    return res;
}
vl factorize(ll n) {
    auto res = inner_factorize(n);
    sort(all(res));
    return res;
}
map<ll, ll> factor_count(ll n) {
    auto res = inner_factorize(n);
    map<ll, ll> mp;
    for(auto &x : res) {
        mp[x]++;
    }
    return mp;
}
vl divisors(ll n) {
    vl res = {1};
    auto mp = factor_count(n);
    for(auto [p, cnt] : mp) {
        ll sz = ssize(res);
        rep(i, sz) {
            ll pi = p;
            rep(_, cnt) {
                res.push_back(res[i] * pi);
                if(_ + 1 != cnt)
                    pi *= p;
            }
        }
    }
    sort(all(res));
    return res;
}
} // namespace fast_factorize
using fast_factorize::divisors;
using fast_factorize::factor_count;
using fast_factorize::factorize;
#line 3 "/home/y_midori/cp/04_yukicoder/457/b.cpp"
#include <atcoder/math>
// #include <atcoder/all>
// using namespace atcoder;
// using mint = modint998244353;
ll kerm(ll n) {
    auto pe = factor_count(n);
    ll res = 1;
    for(auto [p, e] : pe) {
        if(p == 2) {
            if(e == 2)
                res = lcm(res, 2);
            else if(e >= 3) {
                res = lcm(res, 1ll << (e - 2));
            }
        } else {
            ll k = p - 1;
            rep(i, e - 1) k *= p;
            res = lcm(res, k);
        }
    }
    debug(n, res);
    return res;
}
void solve() {
    LL(mod);
    if(mod == 1) {
        print(1);
        return;
    }
    auto d = divisors(kerm(mod));
    ll ans = inf;
    for(auto di : d) {
        rep(j, 1, 7) if(atcoder::pow_mod(10, j * di, mod) == 1)
            chmin(ans, j * di);
    }
    print(ans);
    // ll t = 10;
    // rep(i, 1, inf) {
    //     if(t == 1) {
    //         print(i);
    //         return;
    //     }
    //     t = (t * 10) % mod;
    // }
}
int main() {
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cout << std::setprecision(16);
    int t = 1;
    rep(_, t) {
        solve();
    }
}
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