#831142 (C++17) No.2181 LRM Question 2

• 問題: No.2181 LRM Question 2
• ユーザー: tokusakurai
• 提出日時: 2023-01-06 23:32:54
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: TLE
• 実行時間: -
• コード長: 18,077 bytes
• コンパイル時間: 2,644 ms
• コンパイル使用メモリ: 216,116 KB
• 最終ジャッジ日時: 2025-02-10 00:29:21
• ジャッジサーバーID （参考情報）: judge4 / judge2

ファイルパターン	結果
sample	AC * 3
other	AC * 16 WA * 3 TLE * 4

ソースコード

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;

template <typename T>
using maxheap = priority_queue<T>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
// const int MOD = 1000000007;
const int MOD = 998244353;

struct Runtime_Mod_Int {
    int x;

    Runtime_Mod_Int() : x(0) {}

    Runtime_Mod_Int(long long y) {
        x = y % get_mod();
        if (x < 0) x += get_mod();
    }

    static inline int &get_mod() {
        static int mod = 0;
        return mod;
    }

    static void set_mod(int md) { get_mod() = md; }

    Runtime_Mod_Int &operator+=(const Runtime_Mod_Int &p) {
        if ((x += p.x) >= get_mod()) x -= get_mod();
        return *this;
    }

    Runtime_Mod_Int &operator-=(const Runtime_Mod_Int &p) {
        if ((x += get_mod() - p.x) >= get_mod()) x -= get_mod();
        return *this;
    }

    Runtime_Mod_Int &operator*=(const Runtime_Mod_Int &p) {
        x = (int)(1LL * x * p.x % get_mod());
        return *this;
    }

    Runtime_Mod_Int &operator/=(const Runtime_Mod_Int &p) {
        *this *= p.inverse();
        return *this;
    }

    Runtime_Mod_Int &operator++() { return *this += Runtime_Mod_Int(1); }

    Runtime_Mod_Int operator++(int) {
        Runtime_Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Runtime_Mod_Int &operator--() { return *this -= Runtime_Mod_Int(1); }

    Runtime_Mod_Int operator--(int) {
        Runtime_Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

    Runtime_Mod_Int operator-() const { return Runtime_Mod_Int(-x); }

    Runtime_Mod_Int operator+(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) += p; }

    Runtime_Mod_Int operator-(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) -= p; }

    Runtime_Mod_Int operator*(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) *= p; }

    Runtime_Mod_Int operator/(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) /= p; }

    bool operator==(const Runtime_Mod_Int &p) const { return x == p.x; }

    bool operator!=(const Runtime_Mod_Int &p) const { return x != p.x; }

    Runtime_Mod_Int inverse() const {
        assert(*this != Runtime_Mod_Int(0));
        return pow(get_mod() - 2);
    }

    Runtime_Mod_Int pow(long long k) const {
        Runtime_Mod_Int now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const Runtime_Mod_Int &p) { return os << p.x; }

    friend istream &operator>>(istream &is, Runtime_Mod_Int &p) {
        long long a;
        is >> a;
        p = Runtime_Mod_Int(a);
        return is;
    }
};

using mint = Runtime_Mod_Int;

template <typename T>
struct Combination {
    static vector<T> _fac, _ifac;

    Combination() {}

    static void init(int n) {
        _fac.resize(n + 1), _ifac.resize(n + 1);
        _fac[0] = 1;
        for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i;
        _ifac[n] = _fac[n].inverse();
        for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i;
    }

    static T fac(int k) { return _fac[k]; }

    static T ifac(int k) { return _ifac[k]; }

    static T inv(int k) { return fac(k - 1) * ifac(k); }

    static T P(int n, int k) {
        if (k < 0 || n < k) return 0;
        return fac(n) * ifac(n - k);
    }

    static T C(int n, int k) {
        if (k < 0 || n < k) return 0;
        return fac(n) * ifac(n - k) * ifac(k);
    }

    // k 個の区別できない玉を n 個の区別できる箱に入れる場合の数
    static T H(int n, int k) {
        if (n < 0 || k < 0) return 0;
        return k == 0 ? 1 : C(n + k - 1, k);
    }

    // n 個の区別できる玉を、k 個の区別しない箱に、各箱に 1 個以上玉が入るように入れる場合の数
    static T second_stirling_number(int n, int k) {
        T ret = 0;
        for (int i = 0; i <= k; i++) {
            T tmp = C(k, i) * T(i).pow(n);
            ret += ((k - i) & 1) ? -tmp : tmp;
        }
        return ret * ifac(k);
    }

    // n 個の区別できる玉を、k 個の区別しない箱に入れる場合の数
    static T bell_number(int n, int k) {
        if (n == 0) return 1;
        k = min(k, n);
        vector<T> pref(k + 1);
        pref[0] = 1;
        for (int i = 1; i <= k; i++) {
            if (i & 1) {
                pref[i] = pref[i - 1] - ifac(i);
            } else {
                pref[i] = pref[i - 1] + ifac(i);
            }
        }
        T ret = 0;
        for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i];
        return ret;
    }
};

template <typename T>
vector<T> Combination<T>::_fac = vector<T>();

template <typename T>
vector<T> Combination<T>::_ifac = vector<T>();

template <typename T>
vector<T> divisors(const T &n) {
    vector<T> ret;
    for (T i = 1; i * i <= n; i++) {
        if (n % i == 0) {
            ret.push_back(i);
            if (i * i != n) ret.push_back(n / i);
        }
    }
    sort(begin(ret), end(ret));
    return ret;
}

template <typename T>
vector<pair<T, int>> prime_factor(T n) {
    vector<pair<T, int>> ret;
    for (T i = 2; i * i <= n; i++) {
        int cnt = 0;
        while (n % i == 0) cnt++, n /= i;
        if (cnt > 0) ret.emplace_back(i, cnt);
    }
    if (n > 1) ret.emplace_back(n, 1);
    return ret;
}

template <typename T>
bool is_prime(const T &n) {
    if (n == 1) return false;
    for (T i = 2; i * i <= n; i++) {
        if (n % i == 0) return false;
    }
    return true;
}

// 1,2,...,n のうち k と互いに素である自然数の個数
template <typename T>
T coprime(T n, T k) {
    vector<pair<T, int>> ps = prime_factor(k);
    int m = ps.size();
    T ret = 0;
    for (int i = 0; i < (1 << m); i++) {
        T prd = 1;
        for (int j = 0; j < m; j++) {
            if ((i >> j) & 1) prd *= ps[j].first;
        }
        ret += (__builtin_parity(i) ? -1 : 1) * (n / prd);
    }
    return ret;
}

vector<bool> Eratosthenes(const int &n) {
    vector<bool> ret(n + 1, true);
    if (n >= 0) ret[0] = false;
    if (n >= 1) ret[1] = false;
    for (int i = 2; i * i <= n; i++) {
        if (!ret[i]) continue;
        for (int j = i + i; j <= n; j += i) ret[j] = false;
    }
    return ret;
}

vector<int> Eratosthenes2(const int &n) {
    vector<int> ret(n + 1);
    iota(begin(ret), end(ret), 0);
    if (n >= 0) ret[0] = -1;
    if (n >= 1) ret[1] = -1;
    for (int i = 2; i * i <= n; i++) {
        if (ret[i] < i) continue;
        for (int j = i + i; j <= n; j += i) ret[j] = min(ret[j], i);
    }
    return ret;
}

struct Random_Number_Generator {
    mt19937_64 mt;

    Random_Number_Generator() : mt(chrono::steady_clock::now().time_since_epoch().count()) {}

    // [l,r) での一様乱数
    int64_t operator()(int64_t l, int64_t r) {
        uniform_int_distribution<int64_t> dist(l, r - 1);
        return dist(mt);
    }

    // [0,r) での一様乱数
    int64_t operator()(int64_t r) { return (*this)(0, r); }
} rng;

long long modpow(long long x, long long n, const int &m) {
    x %= m;
    long long ret = 1;
    for (; n > 0; n >>= 1, x *= x, x %= m) {
        if (n & 1) ret *= x, ret %= m;
    }
    return ret;
}

template <typename T>
T modinv(T a, const T &m) {
    T b = m, u = 1, v = 0;
    while (b > 0) {
        T t = a / b;
        swap(a -= t * b, b);
        swap(u -= t * v, v);
    }
    return u >= 0 ? u % m : (m - (-u) % m) % m;
}

// オイラーの φ 関数 (x と m が互いに素ならば、x^φ(m) ≡ 1 (mod m))
template <typename T>
T Euler_totient(T m) {
    T ret = m;
    for (T i = 2; i * i <= m; i++) {
        if (m % i == 0) ret /= i, ret *= i - 1;
        while (m % i == 0) m /= i;
    }
    if (m > 1) ret /= m, ret *= m - 1;
    return ret;
}

// x^k ≡ y (mod m) となる最小の非負整数 k (存在しなければ -1)
int modlog(int x, int y, int m, int max_ans = -1) {
    if (max_ans == -1) max_ans = m;
    long long g = 1;
    for (int i = m; i > 0; i >>= 1) g *= x, g %= m;
    g = gcd(g, m);
    int c = 0;
    long long t = 1;
    for (; t % g != 0; c++) {
        if (t == y) return c;
        t *= x, t %= m;
    }
    if (y % g != 0) return -1;
    t /= g, y /= g, m /= g;
    int n = 0;
    long long gs = 1;
    for (; n * n < max_ans; n++) gs *= x, gs %= m;
    unordered_map<int, int> mp;
    long long e = y;
    for (int i = 0; i < n; mp[e] = ++i) e *= x, e %= m;
    e = t;
    for (int i = 0; i < n; i++) {
        e *= gs, e %= m;
        if (mp.count(e)) return c + n * (i + 1) - mp[e];
    }
    return -1;
}

// x^k ≡ 1 (mod m) となる最小の正整数 k (x と m は互いに素)
template <typename T>
T order(T x, const T &m) {
    T n = Euler_totient(m);
    vector<T> ds;
    for (T i = 1; i * i <= n; i++) {
        if (n % i == 0) ds.push_back(i), ds.push_back(n / i);
    }
    sort(begin(ds), end(ds));
    for (auto &e : ds) {
        if (modpow(x, e, m) == 1) return e;
    }
    return -1;
}

// 素数 p の原始根
template <typename T>
T primitive_root(const T &p) {
    vector<T> ds;
    for (T i = 1; i * i <= p - 1; i++) {
        if ((p - 1) % i == 0) ds.push_back(i), ds.push_back((p - 1) / i);
    }
    sort(begin(ds), end(ds));
    while (true) {
        T r = rng(1, p);
        for (auto &e : ds) {
            if (e == p - 1) return r;
            if (modpow(r, e, p) == 1) break;
        }
    }
}

template <typename T>
T _gcd(const T &a, const T &b) {
    if (b == 0) return a;
    return _gcd(b, a % b);
}

template <typename T>
T _lcm(const T &a, const T &b) {
    return a * (b / _gcd(a, b));
}

// |x| と |y| は結果として max(a,b) 以下になる。
template <typename T>
T extgcd(const T &a, const T &b, T &x, T &y) {
    if (b == 0) {
        x = 1, y = 0;
        return a;
    }
    T g = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
    return g;
}

int mod(const long long &a, const int &m) {
    int ret = a % m;
    return ret + (ret < 0 ? m : 0);
}

// a と m は互いに素
int modinv(const int &a, const int &m) {
    int x, y;
    extgcd(a, m, x, y);
    return mod(x, m);
}

// Σ[0<=i<n] floor((ai+b)/m)
template <typename T>
T floor_sum(const T &n, const T &m, T a, T b) {
    T ret = (a / m) * (n * (n - 1) / 2) + (b / m) * n;
    a %= m, b %= m;
    T y = (a * n + b) / m;
    if (y == 0) return ret;
    ret += floor_sum(y, a, m, a * n - (m * y - b));
    return ret;
}

// min{ai+b mod m | 0<=i<n} またがないときコスト p, またぐときコスト q
template <typename T>
T linear_mod_min(T n, const T &m, T a, T b, bool is_min = true, T p = 1, T q = 1) {
    if (a == 0) return b;
    if (is_min) {
        if (b >= a) {
            T t = (m - b + a - 1) / a;
            T c = (t - 1) * p + q;
            if (n <= c) return b;
            n -= c;
            b += a * t - m;
        }
        b = a - 1 - b;
    } else {
        if (b < m - a) {
            T t = (m - b - 1) / a;
            T c = t * p;
            if (n <= c) return a * ((n - 1) / p) + b;
            n -= c;
            b += a * t;
        }
        b = m - 1 - b;
    }
    T d = m / a;
    T c = linear_mod_min(n, a, m % a, b, !is_min, (d - 1) * p + q, d * p + q);
    return is_min ? a - 1 - c : m - 1 - c;
}

template <typename T>
pair<T, T> Chinese_remainder_theorem(const T &a1, const T &m1, const T &a2, const T &m2) {
    T x, y, g = extgcd(m1, m2, x, y);
    if ((a2 - a1) % g != 0) return make_pair(0, -1);
    T m = m1 * (m2 / g);
    T tmp = mod(x * ((a2 - a1) / g), m2 / g);
    T a = (m1 * tmp + a1) % m;
    return make_pair(a, m);
}

// m の各要素がそれぞれ互いに素とは限らない場合の前処理
bool prepare_Garner(vector<int> &a, vector<int> &m) {
    int n = a.size();
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < i; j++) {
            int g = gcd(m[i], m[j]);
            if ((a[i] - a[j]) % g != 0) return false;
            m[i] /= g, m[j] /= g;
            int gi = gcd(m[i], g), gj = g / gi;
            do {
                g = gcd(gi, gj);
                gi *= g, gj /= g;
            } while (g > 1);
            m[i] *= gi, m[j] *= gj;
        }
    }
    return true;
}

// m の各要素はそれぞれ互いに素
int Garner(vector<int> a, vector<int> m, const int &M) {
    m.push_back(M);
    vector<long long> coeffs(m.size(), 1);
    vector<long long> constants(m.size(), 0);
    for (int k = 0; k < (int)a.size(); k++) {
        long long x = a[k] - constants[k], y = modinv(coeffs[k], m[k]);
        long long t = mod(x * y, m[k]);
        for (int i = k + 1; i < (int)m.size(); i++) {
            constants[i] += t * coeffs[i], constants[i] %= m[i];
            coeffs[i] *= m[k], coeffs[i] %= m[i];
        }
    }
    return constants.back();
}

int main() {
    ll L, R, M;
    cin >> L >> R >> M;

    if (M == 1) {
        cout << "0\n";
        return 0;
    }

    auto ps = prime_factor(M);
    // vector<ll> p;
    // each(e, ps) p.eb(e.first);
    // int K = sz(p);

    // vector<vector<ll>> fac(K), ifac(K);

    // rep(i, K) {
    //     fac[i].assign(p[i], 1);
    //     rep2(j, 1, p[i]) fac[i][j] = fac[i][j - 1] * j % p[i];
    //     ifac[i].assign(p[i], 1);
    //     ifac[i][p[i] - 1] = modinv(fac[i][p[i] - 1], p[i]);
    //     per2(j, 1, p[i]) ifac[i][j - 1] = ifac[i][j] * j % p[i];
    // }

    // ll ans = 0;

    // auto comb = [&](int i, int n, int k) {
    //     if (n < k) return 0LL;
    //     return (fac[i][n] * ifac[i][k] * ifac[i][n - k]) % p[i];
    // };

    auto solve = [&](ll l, ll r, ll p, ll c) {
        ll q = 1;
        rep(i, c) q *= p;
        vector<ll> fac(q, 1), ifac(q, 1);
        rep2(i, 1, q) {
            ll x = i;
            while (x % p == 0) x /= p;
            fac[i] = fac[i - 1] * x % q;
            ifac[i] = modinv(fac[i], q);
        }

        auto calc1 = [&](ll n) {
            ll cnt = 0;
            while (n > 0) {
                cnt += n / p;
                n /= p;
            }
            return cnt;
        };

        auto calc2 = [&](ll n) {
            ll ret = 1;
            while (n > 0) {
                ll t = n / q, m = n % q;
                ret *= modpow(fac[q - 1], t, q), ret %= q;
                ret *= fac[m], ret %= q;
                n /= q;
            }
            return ret;
        };

        auto calc3 = [&](ll n) {
            ll ret = 1;
            while (n > 0) {
                ll t = n / q, m = n % q;
                ret *= modpow(ifac[q - 1], t, q), ret %= q;
                ret *= ifac[m], ret %= q;
                n /= q;
            }
            return ret;
        };

        ll ret = 0;
        for (ll n = L; n <= R; n++) {
            ll c1 = calc1(2 * n), m1 = calc2(2 * n);
            ll c2 = calc1(n), m2 = calc3(n);
            // cout << n MM c1 MM m1 MM c2 MM m2 << '\n';
            ll t = min(c1 - c2 * 2, c);
            ll tmp = (m1 * m2 * m2) % q;
            rep(i, t) tmp *= p, tmp %= q;
            ret += tmp, ret %= q;
            // cout << tmp << '\n';
        }

        return ret;
    };

    vector<int> as, ms;
    for (auto [p, c] : ps) {
        // cout << p MM c MM solve(L, R, p, c) << '\n';
        ll q = 1;
        rep(i, c) q *= p;
        as.eb(solve(L, R, p, c));
        ms.eb(q);
    }

    ll ans = Garner(as, ms, M);
    ans += M - ((R - L + 1) * 2) % M;
    ans %= M;

    cout << ans << '\n';
}