結果

問題 No.2983 Christmas Color Grid (Advent Calender ver.)
ユーザー 👑 rin204
提出日時 2024-12-08 00:30:24
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 3,340 ms
コード長 35,317 bytes
コンパイル時間 3,916 ms
コンパイル使用メモリ 278,704 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-12-08 00:30:31
合計ジャッジ時間 5,862 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 64
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 #
プレゼンテーションモードにする

// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
// #define INTERACTIVE
#include <bits/stdc++.h>
using namespace std;
namespace templates {
// type
using ll  = long long;
using ull = unsigned long long;
using Pii = pair<int, int>;
using Pil = pair<int, ll>;
using Pli = pair<ll, int>;
using Pll = pair<ll, ll>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
// clang-format off
#define vec(T, A, ...) vector<T> A(__VA_ARGS__);
#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));
#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));
// clang-format on
// for loop
#define fori1(a) for (ll _ = 0; _ < (a); _++)
#define fori2(i, a) for (ll i = 0; i < (a); i++)
#define fori3(i, a, b) for (ll i = (a); i < (b); i++)
#define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)
// declare and input
// clang-format off
#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);
#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);
#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);
#define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___);
#define VEC(T, A, n) vector<T> A(n); inp(A);
#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);
// clang-format on
// const value
const ll MOD1   = 1000000007;
const ll MOD9   = 998244353;
const double PI = acos(-1);
// other macro
#if !defined(RIN__LOCAL) && !defined(INTERACTIVE)
#define endl "\n"
#endif
#define spa ' '
#define len(A) ll(A.size())
#define all(A) begin(A), end(A)
// function
vector<char> stoc(string &S) {
    int n = S.size();
    vector<char> ret(n);
    for (int i = 0; i < n; i++) ret[i] = S[i];
    return ret;
}
string ctos(vector<char> &S) {
    int n      = S.size();
    string ret = "";
    for (int i = 0; i < n; i++) ret += S[i];
    return ret;
}
template <class T>
auto min(const T &a) {
    return *min_element(all(a));
}
template <class T>
auto max(const T &a) {
    return *max_element(all(a));
}
template <class T, class S>
auto clamp(T &a, const S &l, const S &r) {
    return (a > r ? r : a < l ? l : a);
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
    return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
    return (a > b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chclamp(T &a, const S &l, const S &r) {
    auto b = clamp(a, l, r);
    return (a != b ? a = b, 1 : 0);
}
template <typename T>
T sum(vector<T> &A) {
    T tot = 0;
    for (auto a : A) tot += a;
    return tot;
}
template <typename T>
vector<T> compression(vector<T> X) {
    sort(all(X));
    X.erase(unique(all(X)), X.end());
    return X;
}
// input and output
namespace io {
// __int128_t
std::ostream &operator<<(std::ostream &dest, __int128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        __uint128_t tmp = value < 0 ? -value : value;
        char buffer[128];
        char *d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[tmp % 10];
            tmp /= 10;
        } while (tmp != 0);
        if (value < 0) {
            --d;
            *d = '-';
        }
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}
// vector<T>
template <typename T>
istream &operator>>(istream &is, vector<T> &A) {
    for (auto &a : A) is >> a;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << ' ';
    }
    return os;
}
// vector<vector<T>>
template <typename T>
istream &operator>>(istream &is, vector<vector<T>> &A) {
    for (auto &a : A) is >> a;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<vector<T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << endl;
    }
    return os;
}
// pair<S, T>
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &A) {
    is >> A.first >> A.second;
    return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, pair<S, T> &A) {
    os << A.first << ' ' << A.second;
    return os;
}
// vector<pair<S, T>>
template <typename S, typename T>
istream &operator>>(istream &is, vector<pair<S, T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        is >> A[i];
    }
    return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, vector<pair<S, T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << endl;
    }
    return os;
}
// tuple
template <typename T, size_t N>
struct TuplePrint {
    static ostream &print(ostream &os, const T &t) {
        TuplePrint<T, N - 1>::print(os, t);
        os << ' ' << get<N - 1>(t);
        return os;
    }
};
template <typename T>
struct TuplePrint<T, 1> {
    static ostream &print(ostream &os, const T &t) {
        os << get<0>(t);
        return os;
    }
};
template <typename... Args>
ostream &operator<<(ostream &os, const tuple<Args...> &t) {
    TuplePrint<decltype(t), sizeof...(Args)>::print(os, t);
    return os;
}
// io functions
void FLUSH() {
    cout << flush;
}
void print() {
    cout << endl;
}
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
    cout << head;
    if (sizeof...(Tail)) cout << spa;
    print(std::forward<Tail>(tail)...);
}
template <typename T, typename S>
void prisep(vector<T> &A, S sep) {
    int n = A.size();
    for (int i = 0; i < n; i++) {
        cout << A[i];
        if (i != n - 1) cout << sep;
    }
    cout << endl;
}
template <typename T, typename S>
void priend(T A, S end) {
    cout << A << end;
}
template <typename T>
void prispa(T A) {
    priend(A, spa);
}
template <typename T, typename S>
bool printif(bool f, T A, S B) {
    if (f)
        print(A);
    else
        print(B);
    return f;
}
template <class... T>
void inp(T &...a) {
    (cin >> ... >> a);
}
} // namespace io
using namespace io;
// read graph
vector<vector<int>> read_edges(int n, int m, bool direct = false, int indexed = 1) {
    vector<vector<int>> edges(n, vector<int>());
    for (int i = 0; i < m; i++) {
        INT(u, v);
        u -= indexed;
        v -= indexed;
        edges[u].push_back(v);
        if (!direct) edges[v].push_back(u);
    }
    return edges;
}
vector<vector<int>> read_tree(int n, int indexed = 1) {
    return read_edges(n, n - 1, false, indexed);
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wedges(int n, int m, bool direct = false, int indexed = 1) {
    vector<vector<pair<int, T>>> edges(n, vector<pair<int, T>>());
    for (int i = 0; i < m; i++) {
        INT(u, v);
        T w;
        inp(w);
        u -= indexed;
        v -= indexed;
        edges[u].push_back({v, w});
        if (!direct) edges[v].push_back({u, w});
    }
    return edges;
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wtree(int n, int indexed = 1) {
    return read_wedges<T>(n, n - 1, false, indexed);
}
// yes / no
namespace yesno {
// yes
inline bool yes(bool f = true) {
    cout << (f ? "yes" : "no") << endl;
    return f;
}
inline bool Yes(bool f = true) {
    cout << (f ? "Yes" : "No") << endl;
    return f;
}
inline bool YES(bool f = true) {
    cout << (f ? "YES" : "NO") << endl;
    return f;
}
// no
inline bool no(bool f = true) {
    cout << (!f ? "yes" : "no") << endl;
    return f;
}
inline bool No(bool f = true) {
    cout << (!f ? "Yes" : "No") << endl;
    return f;
}
inline bool NO(bool f = true) {
    cout << (!f ? "YES" : "NO") << endl;
    return f;
}
// possible
inline bool possible(bool f = true) {
    cout << (f ? "possible" : "impossible") << endl;
    return f;
}
inline bool Possible(bool f = true) {
    cout << (f ? "Possible" : "Impossible") << endl;
    return f;
}
inline bool POSSIBLE(bool f = true) {
    cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
    return f;
}
// impossible
inline bool impossible(bool f = true) {
    cout << (!f ? "possible" : "impossible") << endl;
    return f;
}
inline bool Impossible(bool f = true) {
    cout << (!f ? "Possible" : "Impossible") << endl;
    return f;
}
inline bool IMPOSSIBLE(bool f = true) {
    cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
    return f;
}
// Alice Bob
inline bool Alice(bool f = true) {
    cout << (f ? "Alice" : "Bob") << endl;
    return f;
}
inline bool Bob(bool f = true) {
    cout << (f ? "Bob" : "Alice") << endl;
    return f;
}
// Takahashi Aoki
inline bool Takahashi(bool f = true) {
    cout << (f ? "Takahashi" : "Aoki") << endl;
    return f;
}
inline bool Aoki(bool f = true) {
    cout << (f ? "Aoki" : "Takahashi") << endl;
    return f;
}
} // namespace yesno
using namespace yesno;
} // namespace templates
using namespace templates;
template <int MOD>
struct Modint {
    int x;
    Modint() : x(0) {}
    Modint(int64_t y) {
        if (y >= 0)
            x = y % MOD;
        else
            x = (y % MOD + MOD) % MOD;
    }
    Modint &operator+=(const Modint &p) {
        x += p.x;
        if (x >= MOD) x -= MOD;
        return *this;
    }
    Modint &operator-=(const Modint &p) {
        x -= p.x;
        if (x < 0) x += MOD;
        return *this;
    }
    Modint &operator*=(const Modint &p) {
        x = int(1LL * x * p.x % MOD);
        return *this;
    }
    Modint &operator/=(const Modint &p) {
        *this *= p.inverse();
        return *this;
    }
    Modint &operator%=(const Modint &p) {
        assert(p.x == 0);
        return *this;
    }
    Modint operator-() const {
        return Modint(-x);
    }
    Modint &operator++() {
        x++;
        if (x == MOD) x = 0;
        return *this;
    }
    Modint &operator--() {
        if (x == 0) x = MOD;
        x--;
        return *this;
    }
    Modint operator++(int) {
        Modint result = *this;
        ++*this;
        return result;
    }
    Modint operator--(int) {
        Modint result = *this;
        --*this;
        return result;
    }
    friend Modint operator+(const Modint &lhs, const Modint &rhs) {
        return Modint(lhs) += rhs;
    }
    friend Modint operator-(const Modint &lhs, const Modint &rhs) {
        return Modint(lhs) -= rhs;
    }
    friend Modint operator*(const Modint &lhs, const Modint &rhs) {
        return Modint(lhs) *= rhs;
    }
    friend Modint operator/(const Modint &lhs, const Modint &rhs) {
        return Modint(lhs) /= rhs;
    }
    friend Modint operator%(const Modint &lhs, const Modint &rhs) {
        assert(rhs.x == 0);
        return Modint(lhs);
    }
    bool operator==(const Modint &p) const {
        return x == p.x;
    }
    bool operator!=(const Modint &p) const {
        return x != p.x;
    }
    bool operator<(const Modint &rhs) const {
        return x < rhs.x;
    }
    bool operator<=(const Modint &rhs) const {
        return x <= rhs.x;
    }
    bool operator>(const Modint &rhs) const {
        return x > rhs.x;
    }
    bool operator>=(const Modint &rhs) const {
        return x >= rhs.x;
    }
    Modint inverse() const {
        int a = x, b = MOD, u = 1, v = 0, t;
        while (b > 0) {
            t = a / b;
            a -= t * b;
            u -= t * v;
            std::swap(a, b);
            std::swap(u, v);
        }
        return Modint(u);
    }
    Modint pow(int64_t k) const {
        Modint ret(1);
        Modint y(x);
        while (k > 0) {
            if (k & 1) ret *= y;
            y *= y;
            k >>= 1;
        }
        return ret;
    }
    std::pair<int, int> to_frac(int max_n = 1000) const {
        int y = x;
        for (int i = 1; i <= max_n; i++) {
            if (y <= max_n) {
                return {y, i};
            } else if (MOD - y <= max_n) {
                return {-(MOD - y), i};
            }
            y = (y + x) % MOD;
        }
        return {-1, -1};
    }
    friend std::ostream &operator<<(std::ostream &os, const Modint &p) {
        return os << p.x;
    }
    friend std::istream &operator>>(std::istream &is, Modint &p) {
        int64_t y;
        is >> y;
        p = Modint<MOD>(y);
        return (is);
    }
    static int get_mod() {
        return MOD;
    }
};
struct Arbitrary_Modint {
    int x;
    static int MOD;
    static void set_mod(int mod) {
        MOD = mod;
    }
    Arbitrary_Modint() : x(0) {}
    Arbitrary_Modint(int64_t y) {
        if (y >= 0)
            x = y % MOD;
        else
            x = (y % MOD + MOD) % MOD;
    }
    Arbitrary_Modint &operator+=(const Arbitrary_Modint &p) {
        x += p.x;
        if (x >= MOD) x -= MOD;
        return *this;
    }
    Arbitrary_Modint &operator-=(const Arbitrary_Modint &p) {
        x -= p.x;
        if (x < 0) x += MOD;
        return *this;
    }
    Arbitrary_Modint &operator*=(const Arbitrary_Modint &p) {
        x = int(1LL * x * p.x % MOD);
        return *this;
    }
    Arbitrary_Modint &operator/=(const Arbitrary_Modint &p) {
        *this *= p.inverse();
        return *this;
    }
    Arbitrary_Modint &operator%=(const Arbitrary_Modint &p) {
        assert(p.x == 0);
        return *this;
    }
    Arbitrary_Modint operator-() const {
        return Arbitrary_Modint(-x);
    }
    Arbitrary_Modint &operator++() {
        x++;
        if (x == MOD) x = 0;
        return *this;
    }
    Arbitrary_Modint &operator--() {
        if (x == 0) x = MOD;
        x--;
        return *this;
    }
    Arbitrary_Modint operator++(int) {
        Arbitrary_Modint result = *this;
        ++*this;
        return result;
    }
    Arbitrary_Modint operator--(int) {
        Arbitrary_Modint result = *this;
        --*this;
        return result;
    }
    friend Arbitrary_Modint operator+(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        return Arbitrary_Modint(lhs) += rhs;
    }
    friend Arbitrary_Modint operator-(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        return Arbitrary_Modint(lhs) -= rhs;
    }
    friend Arbitrary_Modint operator*(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        return Arbitrary_Modint(lhs) *= rhs;
    }
    friend Arbitrary_Modint operator/(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        return Arbitrary_Modint(lhs) /= rhs;
    }
    friend Arbitrary_Modint operator%(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        assert(rhs.x == 0);
        return Arbitrary_Modint(lhs);
    }
    bool operator==(const Arbitrary_Modint &p) const {
        return x == p.x;
    }
    bool operator!=(const Arbitrary_Modint &p) const {
        return x != p.x;
    }
    bool operator<(const Arbitrary_Modint &rhs) {
        return x < rhs.x;
    }
    bool operator<=(const Arbitrary_Modint &rhs) {
        return x <= rhs.x;
    }
    bool operator>(const Arbitrary_Modint &rhs) {
        return x > rhs.x;
    }
    bool operator>=(const Arbitrary_Modint &rhs) {
        return x >= rhs.x;
    }
    Arbitrary_Modint inverse() const {
        int a = x, b = MOD, u = 1, v = 0, t;
        while (b > 0) {
            t = a / b;
            a -= t * b;
            u -= t * v;
            std::swap(a, b);
            std::swap(u, v);
        }
        return Arbitrary_Modint(u);
    }
    Arbitrary_Modint pow(int64_t k) const {
        Arbitrary_Modint ret(1);
        Arbitrary_Modint y(x);
        while (k > 0) {
            if (k & 1) ret *= y;
            y *= y;
            k >>= 1;
        }
        return ret;
    }
    friend std::ostream &operator<<(std::ostream &os, const Arbitrary_Modint &p) {
        return os << p.x;
    }
    friend std::istream &operator>>(std::istream &is, Arbitrary_Modint &p) {
        int64_t y;
        is >> y;
        p = Arbitrary_Modint(y);
        return (is);
    }
    static int get_mod() {
        return MOD;
    }
};
int Arbitrary_Modint::MOD = 998244353;
using modint9 = Modint<998244353>;
using modint1 = Modint<1000000007>;
using modint  = Arbitrary_Modint;
using mint    = modint;
void solve() {
    LL(h, w, K, M);
    mint::set_mod(M);
    vec(mint, powK, h * w + 1);
    fori(i, h * w + 1) {
        powK[i] = mint(i).pow(K);
    }
    map<pair<int, int>, vector<int>> cnt;
    cnt[{1, 1}] = {
        0,
        1,
    };
    cnt[{1, 2}] = {
        0,
        2,
        1,
    };
    cnt[{1, 3}] = {
        0,
        5,
        2,
        1,
    };
    cnt[{1, 4}] = {
        0, 12, 5, 2, 1,
    };
    cnt[{1, 5}] = {
        0, 28, 12, 5, 2, 1,
    };
    cnt[{1, 6}] = {
        0, 64, 28, 12, 5, 2, 1,
    };
    cnt[{1, 7}] = {
        0, 144, 64, 28, 12, 5, 2, 1,
    };
    cnt[{1, 8}] = {
        0, 320, 144, 64, 28, 12, 5, 2, 1,
    };
    cnt[{1, 9}] = {
        0, 704, 320, 144, 64, 28, 12, 5, 2, 1,
    };
    cnt[{1, 10}] = {
        0, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
    };
    cnt[{1, 11}] = {
        0, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
    };
    cnt[{1, 12}] = {
        0, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
    };
    cnt[{1, 13}] = {
        0, 15360, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
    };
    cnt[{1, 14}] = {
        0, 32768, 15360, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
    };
    cnt[{1, 15}] = {
        0, 69632, 32768, 15360, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
    };
    cnt[{1, 16}] = {
        0, 147456, 69632, 32768, 15360, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
    };
    cnt[{1, 17}] = {
        0,   311296, 147456, 69632, 32768, 15360, 7168, 3328, 1536,
        704, 320,    144,    64,    28,    12,    5,    2,    1,
    };
    cnt[{1, 18}] = {
        0,   655360, 311296, 147456, 69632, 32768, 15360, 7168, 3328, 1536,
        704, 320,    144,    64,     28,    12,    5,     2,    1,
    };
    cnt[{1, 19}] = {
        0,    1376256, 655360, 311296, 147456, 69632, 32768, 15360, 7168, 3328,
        1536, 704,     320,    144,    64,     28,    12,    5,     2,    1,
    };
    cnt[{1, 20}] = {
        0,    2883584, 1376256, 655360, 311296, 147456, 69632, 32768, 15360, 7168, 3328,
        1536, 704,     320,     144,    64,     28,     12,    5,     2,     1,
    };
    cnt[{1, 21}] = {
        0,    6029312, 2883584, 1376256, 655360, 311296, 147456, 69632, 32768, 15360, 7168,
        3328, 1536,    704,     320,     144,    64,     28,     12,    5,     2,     1,
    };
    cnt[{1, 22}] = {
        0,     12582912, 6029312, 2883584, 1376256, 655360, 311296, 147456,
        69632, 32768,    15360,   7168,    3328,    1536,   704,    320,
        144,   64,       28,      12,      5,       2,      1,
    };
    cnt[{1, 23}] = {
        0,      26214400, 12582912, 6029312, 2883584, 1376256, 655360, 311296,
        147456, 69632,    32768,    15360,   7168,    3328,    1536,   704,
        320,    144,      64,       28,      12,      5,       2,      1,
    };
    cnt[{1, 24}] = {
        0,      54525952, 26214400, 12582912, 6029312, 2883584, 1376256, 655360, 311296,
        147456, 69632,    32768,    15360,    7168,    3328,    1536,    704,    320,
        144,    64,       28,       12,       5,       2,       1,
    };
    cnt[{1, 25}] = {
        0,      113246208, 54525952, 26214400, 12582912, 6029312, 2883584, 1376256, 655360,
        311296, 147456,    69632,    32768,    15360,    7168,    3328,    1536,    704,
        320,    144,       64,       28,       12,       5,       2,       1,
    };
    cnt[{2, 2}] = {
        0, 8, 4, 4, 1,
    };
    cnt[{2, 3}] = {
        0, 40, 17, 14, 10, 6, 1,
    };
    cnt[{2, 4}] = {
        0, 192, 80, 64, 39, 28, 20, 8, 1,
    };
    cnt[{2, 5}] = {
        0, 896, 368, 296, 184, 120, 81, 58, 34, 10, 1,
    };
    cnt[{2, 6}] = {
        0, 4096, 1664, 1344, 856, 560, 368, 240, 167, 112, 52, 12, 1,
    };
    cnt[{2, 7}] = {
        0, 18432, 7424, 6016, 3904, 2568, 1712, 1112, 728, 488, 337, 198, 74, 14, 1,
    };
    cnt[{2, 8}] = {
        0,    81920, 32768, 26624, 17536, 11584, 7816, 5136, 3384,
        2208, 1456,  992,   647,   324,   100,   16,   1,
    };
    cnt[{2, 9}] = {
        0,    360448, 143360, 116736, 77824, 51584, 35136, 23304, 15520, 10232,
        6704, 4392,   2936,   1976,   1169,  498,   130,   18,    1,
    };
    cnt[{2, 10}] = {
        0,     1572864, 622592, 507904, 342016, 227328, 156032, 104256, 70024, 46640, 30888,
        20320, 13304,   8784,   5904,   3792,   1991,   728,    164,    20,    1,
    };
    cnt[{2, 11}] = {
        0,      6815744, 2686976, 2195456, 1490944, 993280, 686080, 461184,
        311872, 209416,  139968,  93048,   61440,   40328,  26480,  17624,
        11672,  6952,    3217,    1022,    202,     22,     1,
    };
    cnt[{2, 12}] = {
        0,      29360128, 11534336, 9437184, 6455296, 4308992, 2992128, 2021376, 1374592,
        929088, 625544,   419408,   279656,  185376,  122088,  80112,   52888,   35200,
        22416,  12160,    4967,     1388,    244,     24,      1,
    };
    cnt[{3, 3}] = {
        0, 400, 144, 106, 84, 69, 52, 32, 9, 1,
    };
    cnt[{3, 4}] = {
        0, 3840, 1360, 952, 705, 550, 445, 360, 270, 164, 62, 12, 1,
    };
    cnt[{3, 5}] = {
        0, 35840, 12544, 8720, 6408, 4897, 3772, 2972, 2371, 1873, 1385, 854, 376, 101, 15, 1,
    };
    cnt[{3, 6}] = {
        0,     327680, 113664, 78592, 57936, 44456, 34161, 26334, 20329, 15846,
        12510, 9758,   7131,   4478,  2164,  714,   149,   18,    1,
    };
    cnt[{3, 7}] = {
        0,     2949120, 1015808, 699392, 516864, 398928, 308296, 238385, 183352, 140476, 108244,
        84130, 65926,   50898,   36946,  23558,  12123,  4602,   1205,   206,    21,     1,
    };
    cnt[{3, 8}] = {
        0,       26214400, 8978432, 6160384, 4561920, 3537664, 2748496, 2136040, 1652625,
        1269794, 973997,   746362,  574842,  446028,  347449,  266040,  192322,  124150,
        66909,   28072,    8654,    1876,    272,     24,      1,
    };
    cnt[{4, 4}] = {
        0,    73728, 25600, 17152, 11728, 9040, 7504, 6288, 5340,
        4436, 3432,  2360,  1296,  492,   116,  16,   1,
    };
    cnt[{4, 5}] = {
        0,     1376256, 471040, 314368, 213248, 158976, 128272, 105936, 89480, 75998, 64363,
        53486, 42473,   31078,  19942,  10358,  3972,   1054,   186,    20,    1,
    };
    cnt[{4, 6}] = {
        0,       25165824, 8519680, 5668864, 3856384, 2863104, 2288896, 1868032, 1553240,
        1299184, 1090650,  919360,  774295,  643000,  517972,  394544,  274893,  167464,
        83894,   32492,    9316,    1920,    272,     24,      1,
    };
    cnt[{5, 5}] = {
        0,       51380224, 17301504, 11501568, 7749632, 5599232, 4361216, 3564416, 3023760,
        2603088, 2265120,  1971974,  1703398,  1448460, 1194986, 939036,  687581,  454452,
        258314,  119182,   42437,    11295,    2192,    296,     25,      1,
    };
    if (false) {
        vector<int> di = {0, 1, 0, -1};
        vector<int> dj = {1, 0, -1, 0};
        fori(h, 1, 26) fori(w, h, 26) {
            if (h * w > 25) break;
            vec(ll, cnt, h * w + 1);
            vvec(int, A, h, w);
            stack<Pii> st;
            fori(bit, 1 << (h * w)) {
                fori(i, h) fori(j, w) {
                    A[i][j] = (bit >> (i * w + j)) & 1;
                }
                mint tot = 0;
                fori(i, h) fori(j, w) {
                    if (A[i][j] == 0) continue;
                    ll now = 0;
                    st.push({i, j});
                    A[i][j] = 0;
                    now     = 1;
                    while (!st.empty()) {
                        auto [ci, cj] = st.top();
                        st.pop();
                        fori(d, 4) {
                            int ni = ci + di[d];
                            int nj = cj + dj[d];
                            if (ni < 0 or ni >= h or nj < 0 or nj >= w) continue;
                            if (A[ni][nj] == 0) continue;
                            st.push({ni, nj});
                            A[ni][nj] = 0;
                            now++;
                        }
                    }
                    cnt[now]++;
                    tot += powK[now];
                }
                // dp[bit] = tot;
            }
            print("cnt[{", h, ", ", w, "}]={");
            for (auto c : cnt) {
                priend(c, ", ");
            }
            print("};");
        }
    }
    mint all_ = 0;
    if (h > w) swap(h, w);
    fori(i, h * w + 1) {
        ll v = cnt[{h, w}][i];
        all_ += powK[i] * v;
    }
    all_ /= mint(2).pow(h * w);
    mint ans = 0;
    fori(i, 1, h * w + 1) {
        ans += all_ / i;
    }
    print(ans);
}
int main() {
#ifndef INTERACTIVE
    std::cin.tie(0)->sync_with_stdio(0);
#endif
    // std::cout << std::fixed << std::setprecision(12);
    int t;
    t = 1;
    // std::cin >> t;
    while (t--) solve();
    return 0;
}
// // #pragma GCC target("avx2")
// // #pragma GCC optimize("O3")
// // #pragma GCC optimize("unroll-loops")
// // #define INTERACTIVE
//
// #include "kyopro-cpp/template.hpp"
//
// #include "misc/Modint.hpp"
// using mint = modint;
//
// void solve() {
//     LL(h, w, K, M);
//     mint::set_mod(M);
//
//     vec(mint, powK, h * w + 1);
//     fori(i, h * w + 1) {
//         powK[i] = mint(i).pow(K);
//     }
//
//     map<pair<int, int>, vector<int>> cnt;
//
//     cnt[{1, 1}] = {
//         0,
//         1,
//     };
//     cnt[{1, 2}] = {
//         0,
//         2,
//         1,
//     };
//     cnt[{1, 3}] = {
//         0,
//         5,
//         2,
//         1,
//     };
//     cnt[{1, 4}] = {
//         0, 12, 5, 2, 1,
//     };
//     cnt[{1, 5}] = {
//         0, 28, 12, 5, 2, 1,
//     };
//     cnt[{1, 6}] = {
//         0, 64, 28, 12, 5, 2, 1,
//     };
//     cnt[{1, 7}] = {
//         0, 144, 64, 28, 12, 5, 2, 1,
//     };
//     cnt[{1, 8}] = {
//         0, 320, 144, 64, 28, 12, 5, 2, 1,
//     };
//     cnt[{1, 9}] = {
//         0, 704, 320, 144, 64, 28, 12, 5, 2, 1,
//     };
//     cnt[{1, 10}] = {
//         0, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
//     };
//     cnt[{1, 11}] = {
//         0, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
//     };
//     cnt[{1, 12}] = {
//         0, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
//     };
//     cnt[{1, 13}] = {
//         0, 15360, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
//     };
//     cnt[{1, 14}] = {
//         0, 32768, 15360, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
//     };
//     cnt[{1, 15}] = {
//         0, 69632, 32768, 15360, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
//     };
//     cnt[{1, 16}] = {
//         0, 147456, 69632, 32768, 15360, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1,
//     };
//     cnt[{1, 17}] = {
//         0,   311296, 147456, 69632, 32768, 15360, 7168, 3328, 1536,
//         704, 320,    144,    64,    28,    12,    5,    2,    1,
//     };
//     cnt[{1, 18}] = {
//         0,   655360, 311296, 147456, 69632, 32768, 15360, 7168, 3328, 1536,
//         704, 320,    144,    64,     28,    12,    5,     2,    1,
//     };
//     cnt[{1, 19}] = {
//         0,    1376256, 655360, 311296, 147456, 69632, 32768, 15360, 7168, 3328,
//         1536, 704,     320,    144,    64,     28,    12,    5,     2,    1,
//     };
//     cnt[{1, 20}] = {
//         0,    2883584, 1376256, 655360, 311296, 147456, 69632, 32768, 15360, 7168, 3328,
//         1536, 704,     320,     144,    64,     28,     12,    5,     2,     1,
//     };
//     cnt[{1, 21}] = {
//         0,    6029312, 2883584, 1376256, 655360, 311296, 147456, 69632, 32768, 15360, 7168,
//         3328, 1536,    704,     320,     144,    64,     28,     12,    5,     2,     1,
//     };
//     cnt[{1, 22}] = {
//         0,     12582912, 6029312, 2883584, 1376256, 655360, 311296, 147456,
//         69632, 32768,    15360,   7168,    3328,    1536,   704,    320,
//         144,   64,       28,      12,      5,       2,      1,
//     };
//     cnt[{1, 23}] = {
//         0,      26214400, 12582912, 6029312, 2883584, 1376256, 655360, 311296,
//         147456, 69632,    32768,    15360,   7168,    3328,    1536,   704,
//         320,    144,      64,       28,      12,      5,       2,      1,
//     };
//     cnt[{1, 24}] = {
//         0,      54525952, 26214400, 12582912, 6029312, 2883584, 1376256, 655360, 311296,
//         147456, 69632,    32768,    15360,    7168,    3328,    1536,    704,    320,
//         144,    64,       28,       12,       5,       2,       1,
//     };
//     cnt[{1, 25}] = {
//         0,      113246208, 54525952, 26214400, 12582912, 6029312, 2883584, 1376256, 655360,
//         311296, 147456,    69632,    32768,    15360,    7168,    3328,    1536,    704,
//         320,    144,       64,       28,       12,       5,       2,       1,
//     };
//     cnt[{2, 2}] = {
//         0, 8, 4, 4, 1,
//     };
//     cnt[{2, 3}] = {
//         0, 40, 17, 14, 10, 6, 1,
//     };
//     cnt[{2, 4}] = {
//         0, 192, 80, 64, 39, 28, 20, 8, 1,
//     };
//     cnt[{2, 5}] = {
//         0, 896, 368, 296, 184, 120, 81, 58, 34, 10, 1,
//     };
//     cnt[{2, 6}] = {
//         0, 4096, 1664, 1344, 856, 560, 368, 240, 167, 112, 52, 12, 1,
//     };
//     cnt[{2, 7}] = {
//         0, 18432, 7424, 6016, 3904, 2568, 1712, 1112, 728, 488, 337, 198, 74, 14, 1,
//     };
//     cnt[{2, 8}] = {
//         0,    81920, 32768, 26624, 17536, 11584, 7816, 5136, 3384,
//         2208, 1456,  992,   647,   324,   100,   16,   1,
//     };
//     cnt[{2, 9}] = {
//         0,    360448, 143360, 116736, 77824, 51584, 35136, 23304, 15520, 10232,
//         6704, 4392,   2936,   1976,   1169,  498,   130,   18,    1,
//     };
//     cnt[{2, 10}] = {
//         0,     1572864, 622592, 507904, 342016, 227328, 156032, 104256, 70024, 46640, 30888,
//         20320, 13304,   8784,   5904,   3792,   1991,   728,    164,    20,    1,
//     };
//     cnt[{2, 11}] = {
//         0,      6815744, 2686976, 2195456, 1490944, 993280, 686080, 461184,
//         311872, 209416,  139968,  93048,   61440,   40328,  26480,  17624,
//         11672,  6952,    3217,    1022,    202,     22,     1,
//     };
//     cnt[{2, 12}] = {
//         0,      29360128, 11534336, 9437184, 6455296, 4308992, 2992128, 2021376, 1374592,
//         929088, 625544,   419408,   279656,  185376,  122088,  80112,   52888,   35200,
//         22416,  12160,    4967,     1388,    244,     24,      1,
//     };
//     cnt[{3, 3}] = {
//         0, 400, 144, 106, 84, 69, 52, 32, 9, 1,
//     };
//     cnt[{3, 4}] = {
//         0, 3840, 1360, 952, 705, 550, 445, 360, 270, 164, 62, 12, 1,
//     };
//     cnt[{3, 5}] = {
//         0, 35840, 12544, 8720, 6408, 4897, 3772, 2972, 2371, 1873, 1385, 854, 376, 101, 15, 1,
//     };
//     cnt[{3, 6}] = {
//         0,     327680, 113664, 78592, 57936, 44456, 34161, 26334, 20329, 15846,
//         12510, 9758,   7131,   4478,  2164,  714,   149,   18,    1,
//     };
//     cnt[{3, 7}] = {
//         0,     2949120, 1015808, 699392, 516864, 398928, 308296, 238385, 183352, 140476, 108244,
//         84130, 65926,   50898,   36946,  23558,  12123,  4602,   1205,   206,    21,     1,
//     };
//     cnt[{3, 8}] = {
//         0,       26214400, 8978432, 6160384, 4561920, 3537664, 2748496, 2136040, 1652625,
//         1269794, 973997,   746362,  574842,  446028,  347449,  266040,  192322,  124150,
//         66909,   28072,    8654,    1876,    272,     24,      1,
//     };
//     cnt[{4, 4}] = {
//         0,    73728, 25600, 17152, 11728, 9040, 7504, 6288, 5340,
//         4436, 3432,  2360,  1296,  492,   116,  16,   1,
//     };
//     cnt[{4, 5}] = {
//         0,     1376256, 471040, 314368, 213248, 158976, 128272, 105936, 89480, 75998, 64363,
//         53486, 42473,   31078,  19942,  10358,  3972,   1054,   186,    20,    1,
//     };
//     cnt[{4, 6}] = {
//         0,       25165824, 8519680, 5668864, 3856384, 2863104, 2288896, 1868032, 1553240,
//         1299184, 1090650,  919360,  774295,  643000,  517972,  394544,  274893,  167464,
//         83894,   32492,    9316,    1920,    272,     24,      1,
//     };
//     cnt[{5, 5}] = {
//         0,       51380224, 17301504, 11501568, 7749632, 5599232, 4361216, 3564416, 3023760,
//         2603088, 2265120,  1971974,  1703398,  1448460, 1194986, 939036,  687581,  454452,
//         258314,  119182,   42437,    11295,    2192,    296,     25,      1,
//     };
//
//     if (false) {
//         vector<int> di = {0, 1, 0, -1};
//         vector<int> dj = {1, 0, -1, 0};
//
//         fori(h, 1, 26) fori(w, h, 26) {
//             if (h * w > 25) break;
//             vec(ll, cnt, h * w + 1);
//
//             vvec(int, A, h, w);
//             stack<Pii> st;
//             fori(bit, 1 << (h * w)) {
//                 fori(i, h) fori(j, w) {
//                     A[i][j] = (bit >> (i * w + j)) & 1;
//                 }
//
//                 mint tot = 0;
//                 fori(i, h) fori(j, w) {
//                     if (A[i][j] == 0) continue;
//                     ll now = 0;
//                     st.push({i, j});
//                     A[i][j] = 0;
//                     now     = 1;
//                     while (!st.empty()) {
//                         auto [ci, cj] = st.top();
//                         st.pop();
//                         fori(d, 4) {
//                             int ni = ci + di[d];
//                             int nj = cj + dj[d];
//                             if (ni < 0 or ni >= h or nj < 0 or nj >= w) continue;
//                             if (A[ni][nj] == 0) continue;
//                             st.push({ni, nj});
//                             A[ni][nj] = 0;
//                             now++;
//                         }
//                     }
//
//                     cnt[now]++;
//
//                     tot += powK[now];
//                 }
//
//                 // dp[bit] = tot;
//             }
//
//             print("cnt[{", h, ", ", w, "}]={");
//             for (auto c : cnt) {
//                 priend(c, ", ");
//             }
//             print("};");
//         }
//     }
//
//     mint all_ = 0;
//     if (h > w) swap(h, w);
//     fori(i, h * w + 1) {
//         ll v = cnt[{h, w}][i];
//         all_ += powK[i] * v;
//     }
//
//     all_ /= mint(2).pow(h * w);
//     mint ans = 0;
//     fori(i, 1, h * w + 1) {
//         ans += all_ / i;
//     }
//     print(ans);
// }
//
// int main() {
// #ifndef INTERACTIVE
//     std::cin.tie(0)->sync_with_stdio(0);
// #endif
//     // std::cout << std::fixed << std::setprecision(12);
//     int t;
//     t = 1;
//     // std::cin >> t;
//     while (t--) solve();
//     return 0;
// }
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0