#874427 (C++17) No.2327 Inversion Sum

• 問題: No.2327 Inversion Sum
• ユーザー: tomo0608
• 提出日時: 2023-05-28 14:37:31
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 38 ms / 2,000 ms
• コード長: 9,704 bytes
• コンパイル時間: 2,536 ms
• コンパイル使用メモリ: 232,424 KB
• 最終ジャッジ日時: 2025-02-13 11:48:31
• ジャッジサーバーID （参考情報）: judge3 / judge5

ファイルパターン	結果
sample	AC * 3
other	AC * 30

ソースコード

/**
*    author:  tomo0608
*    created: 01.05.2023 18:24:08
**/

#ifdef __LOCAL
#define _GLIBCXX_DEBUG
#endif
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#include <atcoder/modint>

namespace tomo0608 {
    typedef long long ll;
    typedef long double ld;
    template <class T> using V = std::vector<T>;
    template <class T> using VV = V<V<T>>;
    template <class T> using VVV = V<VV<T>>;
    typedef std::pair<int, int> pii;
    typedef std::pair<long long, long long> pll;
    template<class... T>void input(T&... a) { (std::cin >> ... >> a); };

#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 DBL(...) double __VA_ARGS__; input(__VA_ARGS__)
    std::istream& operator>>(std::istream& is, atcoder::modint998244353& a) { long long v; is >> v; a = v; return is; }
    std::ostream& operator<<(std::ostream& os, const atcoder::modint998244353& a) { return os << a.val(); }
    std::istream& operator>>(std::istream& is, atcoder::modint1000000007& a) { long long v; is >> v; a = v; return is; }
    std::ostream& operator<<(std::ostream& os, const atcoder::modint1000000007& a) { return os << a.val(); }
    template<int m> std::istream& operator>>(std::istream& is, atcoder::static_modint<m>& a) { long long v; is >> v; a = v; return is; }
    template<int m> std::ostream& operator<<(std::ostream& os, const atcoder::static_modint<m>& a) { return os << a.val(); }
    template<int m> std::istream& operator>>(std::istream& is, atcoder::dynamic_modint<m>& a) { long long v; is >> v; a = v; return is; }
    template<int m> std::ostream& operator<<(std::ostream& os, const atcoder::dynamic_modint<m>& a) { return os << a.val(); }
    template<class T1, class T2> std::istream& operator>>(std::istream& is, std::pair<T1, T2>& p) { is >> p.first >> p.second; return is; }
    template<class T1, class T2> std::ostream& operator<<(std::ostream& os, const std::pair<T1, T2>& p) { os << '(' << p.first << ", " << p.second << ')'; return os; }
    template<class T> std::istream& operator>>(std::istream& is, std::vector<T>& v) { for (auto& e : v) is >> e; return is; }
    template<class T> std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) { for (auto& e : v) os << e << ' '; return os; }
    template<typename T> std::ostream& operator << (std::ostream& os, std::set<T>& set_var) { os << "{"; for (auto itr = set_var.begin(); itr != set_var.end(); itr++) { os << *itr;++itr;if (itr != set_var.end()) os << ", ";itr--; }os << "}";return os; }
    template <typename T, typename U> std::ostream& operator<<(std::ostream& os, std::map<T, U>& map_var) { os << "{";for (auto itr = map_var.begin(); itr != map_var.end(); itr++) { os << *itr;itr++;if (itr != map_var.end()) os << ", ";itr--; }os << "}";return os; }

    void print() { std::cout << '\n'; }
    template<class T, class... Ts>void print(const T& a, const Ts&... b) { std::cout << a; (std::cout << ... << (std::cout << ' ', b)); std::cout << '\n'; }
    void drop() { std::cout << '\n';exit(0); }
    template<class T, class... Ts>void drop(const T& a, const Ts&... b) { std::cout << a; (std::cout << ... << (std::cout << ' ', b)); std::cout << '\n';exit(0); }
#ifdef __LOCAL
    void debug_out() { std::cerr << std::endl; }
    template < class Head, class... Tail> void debug_out(Head H, Tail... T) { std::cerr << ' ' << H; debug_out(T...); }
#define debug(...) std::cerr << 'L' << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) std::cerr << 'L' << __LINE__ << " " << #x << " = " << (x) << std::endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif


#define rep1(a)          for(long long i = 0; i < a; i++)
#define rep2(i, a)       for(long long i = 0; i < a; i++)
#define rep3(i, a, b)    for(long long i = a; i < b; i++)
#define rep4(i, a, b, c) for(long long i = a; i < b; i += c)
#define drep1(a)          for(long long i = a-1; i >= 0; i--)
#define drep2(i, a)       for(long long i = a-1; i >= 0; i--)
#define drep3(i, a, b)    for(long long i = a-1; i >= b; i--)
#define drep4(i, a, b, c) for(long long i = a-1; i >= b; i -= c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define drep(...) overload4(__VA_ARGS__, drep4, drep3, drep2, drep1)(__VA_ARGS__)

} // namespace tomo0608

int dx[8] = { 1, 0, -1, 0, 1, 1, -1, -1 };
int dy[8] = { 0, 1, 0, -1, 1, -1, -1, 1 };
#define endl '\n'


namespace tomo0608 {
#define all(x) x.begin(),x.end()
    template <class T = long long, class S> T SUM(const S& v) { return accumulate(all(v), T(0)); }
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())
    template <typename T> void zip(std::vector<T>& x) { std::vector<T> y = x;UNIQUE(y);for (int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); } }
    template<class T> using priority_queue_rev = std::priority_queue<T, std::vector<T>, std::greater<T>>;
    template<class T, class U> inline bool chmax(T& a, const U& b) { if (a < b) { a = b; return 1; } return 0; }
    template<class T, class U> inline bool chmin(T& a, const U& b) { if (a > b) { a = b; return 1; } return 0; }
    template<class T> inline int count_between(std::vector<T>& a, T l, T r) { return lower_bound(all(a), r) - lower_bound(all(a), l); } // [l, r)
#define bit(n, k) ((n >> k) & 1) /*nのk bit目*/
    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 lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
    int lowbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
    template <typename T>T mypow(T x, long long n) { T ret = 1;while (n > 0) { if (n & 1)(ret *= x);(x *= x);n >>= 1; }return ret; }
}

//typedef atcoder::modint1000000007 mint;
typedef atcoder::modint998244353 mint;
using namespace atcoder;
using namespace std;
using namespace tomo0608;
#include <atcoder/fenwicktree>


namespace tomo0608 {
    // Binomial Coefficient of modint
    template<class mint> struct BiCoef {
        std::vector<mint> 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].mod();
            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 mint 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 mint perm(int n, int k) const noexcept {
            if (n < k || n < 0 || k < 0)return 0;
            return fact_[n] * finv_[n - k];
        }
        constexpr mint fact(int n) const noexcept {
            if (n < 0)return 0;
            return fact_[n];
        }
        constexpr mint inv(int n) const noexcept {
            if (n < 0)return 0;
            return inv_[n];
        }
        constexpr mint finv(int n) const noexcept {
            if (n < 0)return 0;
            return finv_[n];
        }
        inline mint operator()(int n, int k) { return com(n, k); }

        constexpr mint com_naive(int n, int k) {
            if (n < k || n < 0 || k < 0)return 0;
            mint res = 1;
            k = std::min(k, n - k);
            for (int i = 1; i <= k; i++)res *= inv(i) * (n--);
            return res;
        }

        constexpr mint homo(int n, int r) {
            if (n < 0 || r < 0)return 0;
            return r == 0 ? 1 : com(n + r - 1, r);
        }
    };
} // namespace tomo0608
const ll inf = 1e18;
void solve() {
    LL(n, m);
    BiCoef<mint> B(2 * n + m);
    V<ll> pos(n, -1), pos_inv(n, -1); // pos[i] = 数字iの位置　きまってないなら-1
    V<ll> p_list(m), pos_list(m);
    rep(i, m) {
        LL(p, k);
        pos[--p] = --k;
        pos_inv[k] = p;
        p_list[i] = p;
        pos_list[i] = k;
    }
    sort(all(p_list));
    sort(all(pos_list));
    mint ans = B.com(n - m, 2) * B.fact(n - m) / 2;
    V<ll> v;
    v.reserve(m);
    rep(i, n) {
        if (pos_inv[i] == -1)continue;
        v.emplace_back(pos_inv[i]);
    }
    zip(v);
    fenwick_tree<mint> BIT(m);
    rep(i, m) {
        ans += BIT.sum(v[i] + 1, m) * B.fact(n - m);
        BIT.add(v[i], 1);
    }

    V<ll> left(n), right(n), small(n), big(n); // 数字xの位置がきまってるなら, ひだりのあきみぎのあきちいさいふめいおおきいふめい
    rep(i, m) {
        ll x = p_list[i];
        small[x] = x - i;
        big[x] = (n - m) - small[x];
    }
    rep(i, m) {
        ll now = pos_list[i];
        ll x = pos_inv[now];
        left[x] = now - i;
        right[x] = (n - m) - left[x];
    }
    debug(small);
    debug(big);
    debug(left);
    debug(right);
    rep(i, m) {
        ll x = p_list[i];
        ans += (big[x] * left[x] + small[x] * right[x]) * B.fact(n - m - 1);
    }
    print(ans);
}

int main() {
    std::cin.tie(0);
    std::ios_base::sync_with_stdio(false);
    std::cout << std::setprecision(20);
    int codeforces = 1;
    //cin >> codeforces;
    while (codeforces--) {
        solve();
    }
    return 0;
}