結果

問題 No.8112 区間和係数多項式？
コンテスト
ユーザー torisasami4
提出日時 2024-04-02 02:04:13
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2,434 ms / 6,000 ms
コード長 12,475 bytes
コンパイル時間 2,476 ms
コンパイル使用メモリ 203,316 KB
最終ジャッジ日時 2025-02-20 19:32:11
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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ファイルパターン 結果
other AC * 29
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ソースコード

diff # 

// #define _GLIBCXX_DEBUG
// #pragma GCC optimize("O2,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define per(i, n) for (int i = (n)-1; 0 <= i; i--)
#define rep2(i, l, r) for (int i = (l); i < int(r); i++)
#define per2(i, l, r) for (int i = (r)-1; int(l) <= i; 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()
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';
}
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
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 <class T>
using minheap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <class T>
using maxheap = std::priority_queue<T>;
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));
}

// __int128_t gcd(__int128_t a, __int128_t b) {
//     if (a == 0)
//         return b;
//     if (b == 0)
//         return a;
//     __int128_t cnt = a % b;
//     while (cnt != 0) {
//         a = b;
//         b = cnt;
//         cnt = a % b;
//     }
//     return b;
// }

struct Union_Find_Tree {
    vector<int> data;
    const int n;
    int cnt;

    Union_Find_Tree(int n) : data(n, -1), n(n), cnt(n) {}

    int root(int x) {
        if (data[x] < 0) return x;
        return data[x] = root(data[x]);
    }

    int operator[](int i) { return root(i); }

    bool unite(int x, int y) {
        x = root(x), y = root(y);
        if (x == y) return false;
        // if (data[x] > data[y]) swap(x, y);
        data[x] += data[y], data[y] = x;
        cnt--;
        return true;
    }

    int size(int x) { return -data[root(x)]; }

    int count() { return cnt; };

    bool same(int x, int y) { return root(x) == root(y); }

    void clear() {
        cnt = n;
        fill(begin(data), end(data), -1);
    }
};

template <int mod>
struct Mod_Int {
    int x;

    Mod_Int() : x(0) {}

    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    static int get_mod() { return mod; }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    Mod_Int pow(long long k) const {
        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 Mod_Int &p) {
        return os << p.x;
    }

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

ll mpow(ll x, ll n, ll mod) {
    ll ans = 1;
    x %= mod;
    while (n != 0) {
        if (n & 1) ans = ans * x % mod;
        x = x * x % mod;
        n = n >> 1;
    }
    ans %= mod;
    return ans;
}

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;
}

ll divide_int(ll a, ll b) {
    if (b < 0) a = -a, b = -b;
    return (a >= 0 ? a / b : (a - b + 1) / b);
}

// const int MOD = 1000000007;
const int MOD = 998244353;
using mint = Mod_Int<MOD>;

// ----- library -------
template <typename T>
struct Binary_Indexed_Tree {
    vector<T> bit;
    const int n;

    Binary_Indexed_Tree(const vector<T> &v) : n((int)v.size()) {
        bit.resize(n + 1);
        copy(begin(v), end(v), begin(bit) + 1);
        for (int a = 2; a <= n; a <<= 1) {
            for (int b = a; b <= n; b += a) bit[b] += bit[b - a / 2];
        }
    }

    Binary_Indexed_Tree(int n, const T &x) : Binary_Indexed_Tree(vector<T>(n, x)) {}

    void add(int i, const T &x) {
        for (i++; i <= n; i += (i & -i)) bit[i] += x;
    }

    void change(int i, const T &x) { add(i, x - query(i, i + 1)); }

    T sum(int i) const {
        i = min(i, n);
        if (i <= 0) return 0;
        T ret = 0;
        for (; i > 0; i -= (i & -i)) ret += bit[i];
        return ret;
    }

    T query(int l, int r) const {
        l = max(l, 0), r = min(r, n);
        if (l >= r) return 0;
        return sum(r) - sum(l);
    }

    T operator[](int i) const { return query(i, i + 1); }
};

struct Runtime_Mod_Int1 {
    int x;

    Runtime_Mod_Int1() : x(0) {}

    Runtime_Mod_Int1(long long y) {
        x = y % get_mod();
        if (x < 0) x += get_mod();
    }

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

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

    Runtime_Mod_Int1 &operator+=(const Runtime_Mod_Int1 &p) {
        if ((x += p.x) >= get_mod()) x -= get_mod();
        return *this;
    }

    Runtime_Mod_Int1 &operator-=(const Runtime_Mod_Int1 &p) {
        if ((x += get_mod() - p.x) >= get_mod()) x -= get_mod();
        return *this;
    }

    Runtime_Mod_Int1 &operator*=(const Runtime_Mod_Int1 &p) {
        x = (int)(1LL * x * p.x % get_mod());
        return *this;
    }

    Runtime_Mod_Int1 &operator/=(const Runtime_Mod_Int1 &p) {
        *this *= p.inverse();
        return *this;
    }

    Runtime_Mod_Int1 &operator++() { return *this += Runtime_Mod_Int1(1); }

    Runtime_Mod_Int1 operator++(int) {
        Runtime_Mod_Int1 tmp = *this;
        ++*this;
        return tmp;
    }

    Runtime_Mod_Int1 &operator--() { return *this -= Runtime_Mod_Int1(1); }

    Runtime_Mod_Int1 operator--(int) {
        Runtime_Mod_Int1 tmp = *this;
        --*this;
        return tmp;
    }

    Runtime_Mod_Int1 operator-() const { return Runtime_Mod_Int1(-x); }

    Runtime_Mod_Int1 operator+(const Runtime_Mod_Int1 &p) const { return Runtime_Mod_Int1(*this) += p; }

    Runtime_Mod_Int1 operator-(const Runtime_Mod_Int1 &p) const { return Runtime_Mod_Int1(*this) -= p; }

    Runtime_Mod_Int1 operator*(const Runtime_Mod_Int1 &p) const { return Runtime_Mod_Int1(*this) *= p; }

    Runtime_Mod_Int1 operator/(const Runtime_Mod_Int1 &p) const { return Runtime_Mod_Int1(*this) /= p; }

    bool operator==(const Runtime_Mod_Int1 &p) const { return x == p.x; }

    bool operator!=(const Runtime_Mod_Int1 &p) const { return x != p.x; }

    Runtime_Mod_Int1 inverse() const {
        assert(*this != Runtime_Mod_Int1(0));
        return pow(get_mod() - 2);
    }

    Runtime_Mod_Int1 pow(long long k) const {
        Runtime_Mod_Int1 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_Int1 &p) { return os << p.x; }

    friend istream &operator>>(istream &is, Runtime_Mod_Int1 &p) {
        long long a;
        is >> a;
        p = Runtime_Mod_Int1(a);
        return is;
    }
};

struct Runtime_Mod_Int2 {
    int x;

    Runtime_Mod_Int2() : x(0) {}

    Runtime_Mod_Int2(long long y) {
        x = y % get_mod();
        if (x < 0) x += get_mod();
    }

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

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

    Runtime_Mod_Int2 &operator+=(const Runtime_Mod_Int2 &p) {
        if ((x += p.x) >= get_mod()) x -= get_mod();
        return *this;
    }

    Runtime_Mod_Int2 &operator-=(const Runtime_Mod_Int2 &p) {
        if ((x += get_mod() - p.x) >= get_mod()) x -= get_mod();
        return *this;
    }

    Runtime_Mod_Int2 &operator*=(const Runtime_Mod_Int2 &p) {
        x = (int)(1LL * x * p.x % get_mod());
        return *this;
    }

    Runtime_Mod_Int2 &operator/=(const Runtime_Mod_Int2 &p) {
        *this *= p.inverse();
        return *this;
    }

    Runtime_Mod_Int2 &operator++() { return *this += Runtime_Mod_Int2(1); }

    Runtime_Mod_Int2 operator++(int) {
        Runtime_Mod_Int2 tmp = *this;
        ++*this;
        return tmp;
    }

    Runtime_Mod_Int2 &operator--() { return *this -= Runtime_Mod_Int2(1); }

    Runtime_Mod_Int2 operator--(int) {
        Runtime_Mod_Int2 tmp = *this;
        --*this;
        return tmp;
    }

    Runtime_Mod_Int2 operator-() const { return Runtime_Mod_Int2(-x); }

    Runtime_Mod_Int2 operator+(const Runtime_Mod_Int2 &p) const { return Runtime_Mod_Int2(*this) += p; }

    Runtime_Mod_Int2 operator-(const Runtime_Mod_Int2 &p) const { return Runtime_Mod_Int2(*this) -= p; }

    Runtime_Mod_Int2 operator*(const Runtime_Mod_Int2 &p) const { return Runtime_Mod_Int2(*this) *= p; }

    Runtime_Mod_Int2 operator/(const Runtime_Mod_Int2 &p) const { return Runtime_Mod_Int2(*this) /= p; }

    bool operator==(const Runtime_Mod_Int2 &p) const { return x == p.x; }

    bool operator!=(const Runtime_Mod_Int2 &p) const { return x != p.x; }

    Runtime_Mod_Int2 inverse() const {
        assert(*this != Runtime_Mod_Int2(0));
        return pow(get_mod() - 2);
    }

    Runtime_Mod_Int2 pow(long long k) const {
        Runtime_Mod_Int2 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_Int2 &p) { return os << p.x; }

    friend istream &operator>>(istream &is, Runtime_Mod_Int2 &p) {
        long long a;
        is >> a;
        p = Runtime_Mod_Int2(a);
        return is;
    }
};
// ----- library -------

int main() {
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cout << fixed << setprecision(15);

    int n, b, q;
    cin >> n >> b >> q;
    using modb = Runtime_Mod_Int1;
    modb::set_mod(b);
    vector<int> c(5), d(5);
    rep(k, 5) cin >> c[k] >> d[k];
    vector<modb> a(n);
    a[0] = c[0];
    rep(k, n - 1) a[k + 1] = a[k] * d[0];
    using modn = Runtime_Mod_Int2;
    modn::set_mod(n);
    vector<modn> i(q), j(q);
    vector<modb> x(q), y(q);
    i[0] = c[1];
    j[0] = c[2];
    x[0] = c[3];
    y[0] = c[4];
    rep(k, q - 1) {
        i[k + 1] = i[k] * d[1];
        j[k + 1] = j[k] * d[2];
        x[k + 1] = x[k] * d[3];
        y[k + 1] = y[k] * d[4];
    }
    Binary_Indexed_Tree<modb> bit(a);
    vector<int> p(n);
    rep2(k, 1, n) p[k] = k - (k & (-k));
    rep(k, q) {
        bit.add(i[k].x, x[k] - a[i[k].x]);
        a[i[k].x] = x[k];
        modb ans = 0, po = 1;
        while (1) {
            if (j[k] == 0) {
                ans += a[0] * po;
                break;
            }
            ans += bit.query(p[j[k].x] + 1, j[k].x + 1) * po;
            po *= y[k];
            j[k] = p[j[k].x];
        }
        cout << ans << '\n';
    }
}
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