結果

問題 No.1696 Nonnil
ユーザー rniyarniya
提出日時 2021-10-02 17:07:18
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 563 ms / 3,500 ms
コード長 12,187 bytes
コンパイル時間 2,804 ms
コンパイル使用メモリ 234,112 KB
実行使用メモリ 251,620 KB
最終ジャッジ日時 2024-07-20 11:57:22
合計ジャッジ時間 15,623 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,812 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 2 ms
6,940 KB
testcase_03 AC 426 ms
250,368 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 2 ms
6,944 KB
testcase_06 AC 2 ms
6,944 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 423 ms
250,240 KB
testcase_09 AC 37 ms
18,156 KB
testcase_10 AC 56 ms
26,084 KB
testcase_11 AC 34 ms
14,312 KB
testcase_12 AC 50 ms
24,804 KB
testcase_13 AC 33 ms
14,820 KB
testcase_14 AC 445 ms
220,776 KB
testcase_15 AC 87 ms
33,636 KB
testcase_16 AC 511 ms
251,240 KB
testcase_17 AC 353 ms
200,164 KB
testcase_18 AC 203 ms
99,936 KB
testcase_19 AC 2 ms
6,944 KB
testcase_20 AC 2 ms
6,940 KB
testcase_21 AC 275 ms
157,152 KB
testcase_22 AC 281 ms
149,092 KB
testcase_23 AC 257 ms
133,604 KB
testcase_24 AC 243 ms
123,364 KB
testcase_25 AC 375 ms
193,380 KB
testcase_26 AC 358 ms
198,628 KB
testcase_27 AC 484 ms
245,604 KB
testcase_28 AC 286 ms
137,700 KB
testcase_29 AC 312 ms
175,204 KB
testcase_30 AC 216 ms
118,884 KB
testcase_31 AC 405 ms
213,216 KB
testcase_32 AC 450 ms
233,704 KB
testcase_33 AC 321 ms
160,100 KB
testcase_34 AC 290 ms
165,864 KB
testcase_35 AC 339 ms
186,340 KB
testcase_36 AC 563 ms
251,620 KB
testcase_37 AC 554 ms
251,496 KB
testcase_38 AC 553 ms
251,620 KB
testcase_39 AC 525 ms
250,340 KB
testcase_40 AC 536 ms
249,056 KB
testcase_41 AC 139 ms
48,736 KB
testcase_42 AC 371 ms
218,240 KB
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 # 

#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}

template <int i, typename T> void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {
    if (i) os << ',';
    os << get<i>(t);
    print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {
    os << '{';
    print_tuple<0, tuple<Args...>, Args...>(os, t);
    return os << '}';
}

void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                                   \
    cerr << " ";                                                                     \
    cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
    cerr << " ";                                                                     \
    debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }

template <class T> T ceil(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? x / y : (x - y + 1) / y);
}

template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
#pragma endregion

#include <cassert>
#include <cstdint>
#include <iostream>

template <uint64_t Modulus> class modint {
    using i64 = int64_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

    static_assert(Modulus < static_cast<uint32_t>(1) << 31, "Modulus must be less than 2**31");
    static constexpr u32 mod = Modulus;
    u32 v;

public:
    constexpr modint(const i64 x = 0) noexcept : v(x < 0 ? mod - 1 - (-(x + 1) % mod) : x % mod) {}
    constexpr u32& val() noexcept { return v; }
    constexpr const u32& val() const noexcept { return v; }
    constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; }
    constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; }
    constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; }
    constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; }
    constexpr modint& operator+=(const modint& rhs) noexcept {
        v += rhs.v;
        if (v >= mod) v -= mod;
        return *this;
    }
    constexpr modint& operator-=(const modint& rhs) noexcept {
        if (v < rhs.v) v += mod;
        v -= rhs.v;
        return *this;
    }
    constexpr modint& operator*=(const modint& rhs) noexcept {
        v = (u64)v * rhs.v % mod;
        return *this;
    }
    constexpr modint& operator/=(const modint& rhs) noexcept { return *this *= rhs.inv(); }
    constexpr modint pow(long long n) const noexcept {
        assert(0 <= n);
        modint self(*this), res(1);
        while (n > 0) {
            if (n & 1) res *= self;
            self *= self;
            n >>= 1;
        }
        return res;
    }
    constexpr modint inv() const noexcept {
        assert(*this != 0);
        return pow(mod - 2);
    }
    constexpr modint& operator++() noexcept {
        if (++v == mod) v = 0;
        return *this;
    }
    constexpr modint& operator--() noexcept {
        if (v == 0) v = mod;
        return --v, *this;
    }
    constexpr modint operator++(int) noexcept {
        modint t = *this;
        return ++*this, t;
    }
    constexpr modint operator--(int) noexcept {
        modint t = *this;
        return --*this, t;
    }
    constexpr modint operator-() const noexcept { return modint(mod - v); }
    template <class T> friend constexpr modint operator+(T x, modint y) noexcept { return modint(x) + y; }
    template <class T> friend constexpr modint operator-(T x, modint y) noexcept { return modint(x) - y; }
    template <class T> friend constexpr modint operator*(T x, modint y) noexcept { return modint(x) * y; }
    template <class T> friend constexpr modint operator/(T x, modint y) noexcept { return modint(x) / y; }
    constexpr bool operator==(const modint& rhs) const noexcept { return v == rhs.v; }
    constexpr bool operator!=(const modint& rhs) const noexcept { return v != rhs.v; }
    constexpr bool operator!() const noexcept { return !v; }
    friend std::istream& operator>>(std::istream& s, modint& rhs) noexcept {
        i64 v;
        rhs = modint{(s >> v, v)};
        return s;
    }
    friend std::ostream& operator<<(std::ostream& s, const modint& rhs) noexcept { return s << rhs.v; }
};

/**
 * @brief modint
 * @docs docs/modulo/modint.md
 */

#include <cassert>
#include <vector>

template <typename T> struct Binomial {
    Binomial(int MAX = 0) : n(1), facs(1, T(1)), finvs(1, T(1)), invs(1, T(1)) {
        while (n <= MAX) extend();
    }

    T fac(int i) {
        assert(i >= 0);
        while (n <= i) extend();
        return facs[i];
    }

    T finv(int i) {
        assert(i >= 0);
        while (n <= i) extend();
        return finvs[i];
    }

    T inv(int i) {
        assert(i >= 0);
        while (n <= i) extend();
        return invs[i];
    }

    T P(int n, int r) {
        if (n < 0 || n < r || r < 0) return T(0);
        return fac(n) * finv(n - r);
    }

    T C(int n, int r) {
        if (n < 0 || n < r || r < 0) return T(0);
        return fac(n) * finv(n - r) * finv(r);
    }

    T H(int n, int r) {
        if (n < 0 || r < 0) return T(0);
        return r == 0 ? 1 : C(n + r - 1, r);
    }

    T C_naive(int n, int r) {
        if (n < 0 || n < r || r < 0) return T(0);
        T res = 1;
        r = std::min(r, n - r);
        for (int i = 1; i <= r; i++) res *= inv(i) * (n--);
        return res;
    }

private:
    int n;
    std::vector<T> facs, finvs, invs;

    inline void extend() {
        int m = n << 1;
        facs.resize(m);
        finvs.resize(m);
        invs.resize(m);
        for (int i = n; i < m; i++) facs[i] = facs[i - 1] * i;
        finvs[m - 1] = T(1) / facs[m - 1];
        invs[m - 1] = finvs[m - 1] * facs[m - 2];
        for (int i = m - 2; i >= n; i--) {
            finvs[i] = finvs[i + 1] * (i + 1);
            invs[i] = finvs[i] * facs[i - 1];
        }
        n = m;
    }
};

/**
 * @brief binomial
 * @docs docs/combinatorics/binomial.md
 */

const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
// const long long MOD = 1000000007;
const long long MOD = 998244353;

using mint = modint<MOD>;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N, K;
    cin >> N >> K;
    int M;
    cin >> M;
    vector<pair<int, int>> interval;
    for (; M--;) {
        int L, R;
        cin >> L >> R;
        interval.emplace_back(--L, R);
    }

    vector<int> ban(K, -1);
    {
        sort(interval.begin(), interval.end(), [](const pair<int, int>& a, const pair<int, int>& b) {
            return a.first != b.first ? a.first > b.first : a.second < b.second;
        });
        int min_r = K + 1;
        for (auto& p : interval) {
            if (min_r <= p.second) continue;
            ban[p.first] = p.second;
            min_r = p.second;
        }
    }

    vector<vector<vector<mint>>> dp(K + 1, vector<vector<mint>>(K + 1, vector<mint>(2, 0))),
        rui(K + 2, vector<vector<mint>>(K + 1, vector<mint>(2, 0)));
    vector<vector<mint>> sum(K + 1, vector<mint>(2, 0));
    dp[0][0][0] = rui[1][0][0] = sum[0][0] = 1;
    for (int i = 0; i < K; i++) {
        vector<tuple<int, int, int, mint>> rui_add;
        vector<tuple<int, int, mint>> sum_add;
        if (~ban[i]) {
            for (int j = 0; j < K; j++) {
                for (int k = 0; k < 2; k++) {  // allow ban pick
                    mint add = sum[j][k ^ 1] - rui[i][j][k ^ 1];
                    dp[ban[i]][j][k] += add;
                    rui_add.emplace_back(ban[i] + 1, j, k, add);
                    sum_add.emplace_back(j, k, add);
                }
            }
        }
        for (auto& t : rui_add) {
            int b, j, k;
            mint add;
            tie(b, j, k, add) = t;
            rui[b][j][k] += add;
        }
        for (auto& t : sum_add) {
            int j, k;
            mint add;
            tie(j, k, add) = t;
            sum[j][k] += add;
        }
        for (int j = 0; j < K; j++) {
            for (int k = 0; k < 2; k++) {  // no ban pick
                dp[i + 1][j + 1][k] += dp[i][j][k];
                rui[i + 2][j + 1][k] += dp[i][j][k];
                sum[j + 1][k] += dp[i][j][k];
            }
        }
        for (int j = 0; j <= K; j++) {
            for (int k = 0; k < 2; k++) {
                rui[i + 2][j][k] += rui[i + 1][j][k];
            }
        }
    }

    Binomial<mint> BINOM;
    mint ans = 0;
    for (int j = 0; j <= K; j++) {
        for (int k = 0; k < 2; k++) {
            mint add = dp[K][j][k] * mint(j).pow(N);
            if (!k)
                ans += add;
            else
                ans -= add;
        }
    }

    cout << ans << '\n';
    return 0;
}
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