#544487 (C++17) No.1214 Market

• 問題: No.1214 Market
• ユーザー: yosupot
• 提出日時: 2020-08-30 16:58:53
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 1,165 ms / 2,000 ms
• コード長: 10,828 bytes
• コンパイル時間: 1,753 ms
• コンパイル使用メモリ: 133,384 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-11-15 11:41:15
• 合計ジャッジ時間: 23,432 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	4 ms; 5,248 KB
testcase_01	AC	6 ms; 5,248 KB
testcase_02	AC	6 ms; 5,248 KB
testcase_03	AC	328 ms; 5,248 KB
testcase_04	AC	564 ms; 5,248 KB
testcase_05	AC	778 ms; 5,248 KB
testcase_06	AC	803 ms; 5,248 KB
testcase_07	AC	318 ms; 5,248 KB
testcase_08	AC	1,136 ms; 5,248 KB
testcase_09	AC	1,165 ms; 5,248 KB
testcase_10	AC	1,150 ms; 5,248 KB
testcase_11	AC	1,114 ms; 5,248 KB
testcase_12	AC	1,085 ms; 5,248 KB
testcase_13	AC	1,132 ms; 5,248 KB
testcase_14	AC	1,116 ms; 5,248 KB
testcase_15	AC	1,114 ms; 5,248 KB
testcase_16	AC	1,100 ms; 5,248 KB
testcase_17	AC	1,103 ms; 5,248 KB
testcase_18	AC	878 ms; 5,248 KB
testcase_19	AC	178 ms; 5,248 KB
testcase_20	AC	383 ms; 5,248 KB
testcase_21	AC	111 ms; 5,248 KB
testcase_22	AC	18 ms; 5,248 KB
testcase_23	AC	879 ms; 5,248 KB
testcase_24	AC	178 ms; 5,248 KB
testcase_25	AC	109 ms; 5,248 KB
testcase_26	AC	478 ms; 5,248 KB
testcase_27	AC	237 ms; 5,248 KB
testcase_28	AC	691 ms; 5,248 KB
testcase_29	AC	236 ms; 5,248 KB
testcase_30	AC	202 ms; 5,248 KB
testcase_31	AC	76 ms; 5,248 KB
testcase_32	AC	22 ms; 5,248 KB
testcase_33	AC	492 ms; 5,248 KB
testcase_34	AC	39 ms; 5,248 KB
testcase_35	AC	193 ms; 5,248 KB
testcase_36	AC	304 ms; 5,248 KB
testcase_37	AC	611 ms; 5,248 KB
testcase_38	AC	30 ms; 5,248 KB
testcase_39	AC	4 ms; 5,248 KB
testcase_40	AC	6 ms; 5,248 KB
testcase_41	AC	19 ms; 5,248 KB

ソースコード

//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx")
//#undef LOCAL




#include <algorithm>

#include <array>

#include <bitset>

#include <cassert>

#include <complex>

#include <cstdio>

#include <cstring>

#include <iostream>

#include <map>

#include <numeric>

#include <queue>

#include <set>

#include <string>

#include <unordered_map>

#include <unordered_set>

#include <vector>

using namespace std;

using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;



#include <unistd.h>

struct Scanner {
    int fd = -1;
    char line[(1 << 15) + 1];
    size_t st = 0, ed = 0;
    void reread() {
        memmove(line, line + st, ed - st);
        ed -= st;
        st = 0;
        ed += ::read(fd, line + ed, (1 << 15) - ed);
        line[ed] = '\0';
    }
    bool succ() {
        while (true) {
            if (st == ed) {
                reread();
                if (st == ed) return false;
            }
            while (st != ed && isspace(line[st])) st++;
            if (st != ed) break;
        }
        if (ed - st <= 50) {
            bool sep = false;
            for (size_t i = st; i < ed; i++) {
                if (isspace(line[i])) {
                    sep = true;
                    break;
                }
            }
            if (!sep) reread();
        }
        return true;
    }
    template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
    bool read_single(T& ref) {
        if (!succ()) return false;
        while (true) {
            size_t sz = 0;
            while (st + sz < ed && !isspace(line[st + sz])) sz++;
            ref.append(line + st, sz);
            st += sz;
            if (!sz || st != ed) break;
            reread();
        }
        return true;
    }
    template <class T, enable_if_t<is_integral<T>::value>* = nullptr>
    bool read_single(T& ref) {
        if (!succ()) return false;
        bool neg = false;
        if (line[st] == '-') {
            neg = true;
            st++;
        }
        ref = T(0);
        while (isdigit(line[st])) {
            ref = 10 * ref + (line[st++] & 0xf);
        }
        if (neg) ref = -ref;
        return true;
    }
    template <class T> bool read_single(V<T>& ref) {
        for (auto& d : ref) {
            if (!read_single(d)) return false;
        }
        return true;
    }
    void read() {}
    template <class H, class... T> void read(H& h, T&... t) {
        bool f = read_single(h);
        assert(f);
        read(t...);
    }
    int read_unsafe() { return 0; }
    template <class H, class... T> int read_unsafe(H& h, T&... t) {
        bool f = read_single(h);
        if (!f) return 0;
        return 1 + read_unsafe(t...);
    }
    Scanner(FILE* fp) : fd(fileno(fp)) {}
};

struct Printer {
  public:
    template <bool F = false> void write() {}
    template <bool F = false, class H, class... T>
    void write(const H& h, const T&... t) {
        if (F) write_single(' ');
        write_single(h);
        write<true>(t...);
    }
    template <class... T> void writeln(const T&... t) {
        write(t...);
        write_single('\n');
    }

    Printer(FILE* _fp) : fp(_fp) {}
    ~Printer() { flush(); }

  private:
    static constexpr size_t SIZE = 1 << 15;
    FILE* fp;
    char line[SIZE], small[50];
    size_t pos = 0;
    void flush() {
        fwrite(line, 1, pos, fp);
        pos = 0;
    }
    void write_single(const char& val) {
        if (pos == SIZE) flush();
        line[pos++] = val;
    }
    template <class T, enable_if_t<is_integral<T>::value>* = nullptr>
    void write_single(T val) {
        if (pos > (1 << 15) - 50) flush();
        if (val == 0) {
            write_single('0');
            return;
        }
        if (val < 0) {
            write_single('-');
            val = -val; // todo min
        }
        size_t len = 0;
        while (val) {
            small[len++] = char(0x30 | (val % 10));
            val /= 10;
        }
        for (size_t i = 0; i < len; i++) {
            line[pos + i] = small[len - 1 - i];
        }
        pos += len;
    }
    void write_single(__int128 val) {
        if (pos > (1 << 15) - 50) flush();
        if (val == 0) {
            write_single('0');
            return;
        }
        if (val < 0) {
            write_single('-');
            val = -val; // todo min
        }
        size_t len = 0;
        while (val) {
            small[len++] = char(0x30 | (val % 10));
            val /= 10;
        }
        for (size_t i = 0; i < len; i++) {
            line[pos + i] = small[len - 1 - i];
        }
        pos += len;
    }

    void write_single(const string& s) {
        for (char c : s) write_single(c);
    }
    void write_single(const char* s) {
        size_t len = strlen(s);
        for (size_t i = 0; i < len; i++) write_single(s[i]);
    }
    template <class T> void write_single(const V<T>& val) {
        auto n = val.size();
        for (size_t i = 0; i < n; i++) {
            if (i) write_single(' ');
            write_single(val[i]);
        }
    }
};


template <uint MD> struct ModInt {
    using M = ModInt;
    static constexpr uint get_mod() { return MD; }
    const static M G;
    uint v;
    ModInt(ll _v = 0) { set_v(uint(_v % MD + MD)); }
    M& set_v(uint _v) {
        v = (_v < MD) ? _v : _v - MD;
        return *this;
    }
    explicit operator bool() const { return v != 0; }
    M operator-() const { return M() - *this; }
    M operator+(const M& r) const { return M().set_v(v + r.v); }
    M operator-(const M& r) const { return M().set_v(v + MD - r.v); }
    M operator*(const M& r) const { return M().set_v(uint(ull(v) * r.v % MD)); }
    M operator/(const M& r) const { return *this * r.inv(); }
    M& operator+=(const M& r) { return *this = *this + r; }
    M& operator-=(const M& r) { return *this = *this - r; }
    M& operator*=(const M& r) { return *this = *this * r; }
    M& operator/=(const M& r) { return *this = *this / r; }
    bool operator==(const M& r) const { return v == r.v; }
    M pow(ll n) const {
        M x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    M inv() const { return pow(MD - 2); }
    friend ostream& operator<<(ostream& os, const M& r) { return os << r.v; }
};
// using Mint = ModInt<998244353>;
// template<> const Mint Mint::G = Mint(3);




template <class Mint>
V<Mint> powTable(int n, Mint x) {
    V<Mint> table(n + 1);
    table[0] = Mint(1);
    for (int i = 1; i <= n; i++) {
        table[i] = table[i - 1] * x;
    }
    return table;
}

template<class Mint>
struct Comb {
    int max_n;
    V<Mint> fact, ifact;
    Comb() {}
    Comb(int n) : max_n(n) {
        fact = ifact = V<Mint>(n + 1);
        fact[0] = Mint(1);
        for (int i = 1; i <= n; i++) fact[i] = fact[i - 1] * i;
        ifact[n] = fact[n].inv();
        for (int i = n; i >= 1; i--) ifact[i - 1] = ifact[i] * i;
    }

    Mint C(int n, int k) {
        if (n < k || n < 0) return Mint(0);
        assert(0 <= k && k <= n && n <= max_n);
        return fact[n] * ifact[k] * ifact[n - k];
    }

    // n個の区別出来ないボールをk個の箱に入れる入れ方
    Mint H(int n, int k) {
        if (n == 0 && k == 0) return Mint(1);
        return C(n + k - 1, n);
    }
};
using Mint = ModInt<TEN(9) + 7>;

Comb<Mint> C(100);

Scanner sc = Scanner(stdin);
Printer pr = Printer(stdout);

// (残った人数, lw, mid, up)
Mint dp[42][42][2][42];
Mint ndp[42][42][2][42];
void succ() {
    for (int i = 0; i < 42; i++) {
        for (int j = 0; j < 42; j++) {
            for (int k = 0; k < 2; k++) {
                for (int l = 0; l < 42; l++) {
                    dp[i][j][k][l] = ndp[i][j][k][l];
                    ndp[i][j][k][l] = Mint(0);
                }
            }
        }
    }
}

int main() {
    int n, m, pri;
    sc.read(n, m, pri);
    using P = pair<int, int>;
    V<P> vs(m + 1);
    vs[0] = P(0, 0);
    for (int i = 1; i <= m; i++) {
        sc.read(vs[i].first, vs[i].second);
    }
    m++;
    sort(vs.begin(), vs.end());
    int bk = pri + 1;
    for (int i = m - 1; i >= 0; i--) {
        auto buf = vs[i].first;
        vs[i].first = bk - vs[i].first;
        bk = buf;
    }

    Mint ans = 0;
    for (int trg = 0; trg < m; trg++) {
        P tp = P(vs[trg].second, trg);
        succ(); succ();

        dp[n][0][0][0] = 1;
        int now_j = 0, now_l = 0;
        for (int ph = 0; ph < m; ph++) {
            P now_p = P(vs[ph].second, ph);


            // inc object
            for (int i = 0; i <= n; i++) {
                for (int j = 0; j < 42; j++) {
                    for (int k = 0; k < 2; k++) {
                        for (int l = 0; l < 42; l++) {
                            if (!dp[i][j][k][l].v) continue;
                            int nj = j;
                            int nk = k;
                            int nl = l;
                            if (tp > now_p) nj++;
                            if (tp == now_p) nk++;
                            if (tp < now_p) nl++;
                            ndp[i][nj][nk][nl] += dp[i][j][k][l];
                        }
                    }
                }
            }

            if (tp > now_p) now_j++;
            if (tp < now_p) now_l++;

            succ();

            Mint b = vs[ph].first;

            // inc human
            for (int i = 0; i <= n; i++) {
                for (int w = 0; w <= i; w++) {
                    Mint freq = C.C(i, w) * b.pow(w);
                    for (int j = 0; j <= now_j; j++) {
                        for (int k = 0; k < 2; k++) {
                            for (int l = 0; l <= now_l; l++) {
                                if (!dp[i][j][k][l].v) continue;
                                int z = w;
                                int nl = l - min(l, z);
                                z -= l - nl;
                                int nk = k - min(k, z);
                                z -= k - nk;
                                int nj = j - min(j, z);
                                z -= j - nj;
                                ndp[i - w][nj][nk][nl] += dp[i][j][k][l] * freq;
                            }
                        }
                    }
                }
            }

            succ();
        }

        Mint sum = 0;
        for (int j = 0; j < 42; j++) {
            for (int l = 0; l < 42; l++) {
                sum += dp[0][j][0][l];
            }
        }

                         ;

        ans += sum * vs[trg].second;
    }
            ;
    ans /= Mint(pri + 1).pow(n);
    pr.writeln(ans.v);
    return 0;
}