結果

問題 No.1533 Don't be Negative!
ユーザー tokusakuraitokusakurai
提出日時 2023-07-14 21:17:34
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,278 ms / 8,000 ms
コード長 10,127 bytes
コンパイル時間 2,633 ms
コンパイル使用メモリ 216,840 KB
実行使用メモリ 122,752 KB
最終ジャッジ日時 2024-09-16 06:02:23
合計ジャッジ時間 44,152 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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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 72 ms
17,280 KB
testcase_01 AC 127 ms
34,816 KB
testcase_02 AC 165 ms
42,624 KB
testcase_03 AC 218 ms
46,720 KB
testcase_04 AC 98 ms
27,136 KB
testcase_05 AC 127 ms
34,816 KB
testcase_06 AC 127 ms
34,816 KB
testcase_07 AC 98 ms
27,008 KB
testcase_08 AC 96 ms
27,008 KB
testcase_09 AC 166 ms
42,624 KB
testcase_10 AC 128 ms
34,816 KB
testcase_11 AC 531 ms
69,376 KB
testcase_12 AC 547 ms
66,048 KB
testcase_13 AC 288 ms
37,888 KB
testcase_14 AC 459 ms
54,144 KB
testcase_15 AC 569 ms
68,096 KB
testcase_16 AC 827 ms
90,240 KB
testcase_17 AC 268 ms
35,840 KB
testcase_18 AC 778 ms
86,272 KB
testcase_19 AC 336 ms
51,200 KB
testcase_20 AC 903 ms
96,768 KB
testcase_21 AC 415 ms
57,472 KB
testcase_22 AC 855 ms
92,672 KB
testcase_23 AC 844 ms
91,136 KB
testcase_24 AC 761 ms
84,480 KB
testcase_25 AC 676 ms
79,616 KB
testcase_26 AC 334 ms
54,912 KB
testcase_27 AC 737 ms
82,560 KB
testcase_28 AC 930 ms
98,432 KB
testcase_29 AC 800 ms
88,320 KB
testcase_30 AC 1,217 ms
118,528 KB
testcase_31 AC 203 ms
40,960 KB
testcase_32 AC 410 ms
57,472 KB
testcase_33 AC 959 ms
100,096 KB
testcase_34 AC 143 ms
31,232 KB
testcase_35 AC 888 ms
95,232 KB
testcase_36 AC 840 ms
91,904 KB
testcase_37 AC 389 ms
59,136 KB
testcase_38 AC 1,190 ms
116,480 KB
testcase_39 AC 1,043 ms
106,624 KB
testcase_40 AC 1,088 ms
110,720 KB
testcase_41 AC 961 ms
100,480 KB
testcase_42 AC 1,098 ms
110,464 KB
testcase_43 AC 1,062 ms
108,800 KB
testcase_44 AC 907 ms
96,384 KB
testcase_45 AC 1,015 ms
104,576 KB
testcase_46 AC 1,006 ms
104,704 KB
testcase_47 AC 1,093 ms
110,336 KB
testcase_48 AC 1,064 ms
108,672 KB
testcase_49 AC 1,090 ms
110,720 KB
testcase_50 AC 1,262 ms
122,752 KB
testcase_51 AC 1,210 ms
118,528 KB
testcase_52 AC 1,073 ms
108,288 KB
testcase_53 AC 1,278 ms
122,624 KB
testcase_54 AC 1,275 ms
122,624 KB
testcase_55 AC 1,273 ms
122,624 KB
testcase_56 AC 1,274 ms
122,752 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 # 

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); 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()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;

template <typename T>
using maxheap = priority_queue<T>;

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 <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

int pct(int x) { return __builtin_popcount(x); }
int pct(ll x) { return __builtin_popcountll(x); }
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

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';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

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));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename T>
void reorder(vector<T> &a, const vector<int> &ord) {
    int n = a.size();
    vector<T> b(n);
    for (int i = 0; i < n; i++) b[i] = a[ord[i]];
    swap(a, b);
}

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

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

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

constexpr int inf = (1 << 30) - 1;
constexpr ll INF = (1LL << 60) - 1;
// constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;

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;
    }
};

using mint = Mod_Int<MOD>;

template <typename T>
struct Number_Theoretic_Transform {
    static int max_base;
    static T root;
    static vector<T> r, ir;

    Number_Theoretic_Transform() {}

    static void init() {
        if (!r.empty()) return;
        int mod = T::get_mod();
        int tmp = mod - 1;
        root = 2;
        while (root.pow(tmp >> 1) == 1) root++;
        max_base = 0;
        while (tmp % 2 == 0) tmp >>= 1, max_base++;
        r.resize(max_base), ir.resize(max_base);
        for (int i = 0; i < max_base; i++) {
            r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i]  := 1 の 2^(i+2) 乗根
            ir[i] = r[i].inverse();                 // ir[i] := 1/r[i]
        }
    }

    static void ntt(vector<T> &a) {
        init();
        int n = a.size();
        assert((n & (n - 1)) == 0);
        assert(n <= (1 << max_base));
        for (int k = n; k >>= 1;) {
            T w = 1;
            for (int s = 0, t = 0; s < n; s += 2 * k) {
                for (int i = s, j = s + k; i < s + k; i++, j++) {
                    T x = a[i], y = w * a[j];
                    a[i] = x + y, a[j] = x - y;
                }
                w *= r[__builtin_ctz(++t)];
            }
        }
    }

    static void intt(vector<T> &a) {
        init();
        int n = a.size();
        assert((n & (n - 1)) == 0);
        assert(n <= (1 << max_base));
        for (int k = 1; k < n; k <<= 1) {
            T w = 1;
            for (int s = 0, t = 0; s < n; s += 2 * k) {
                for (int i = s, j = s + k; i < s + k; i++, j++) {
                    T x = a[i], y = a[j];
                    a[i] = x + y, a[j] = w * (x - y);
                }
                w *= ir[__builtin_ctz(++t)];
            }
        }
        T inv = T(n).inverse();
        for (auto &e : a) e *= inv;
    }

    static vector<T> convolve(vector<T> a, vector<T> b) {
        if (a.empty() || b.empty()) return {};
        if (min(a.size(), b.size()) < 40) {
            int n = a.size(), m = b.size();
            vector<T> c(n + m - 1, 0);
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) c[i + j] += a[i] * b[j];
            }
            return c;
        }
        int k = (int)a.size() + (int)b.size() - 1, n = 1;
        while (n < k) n <<= 1;
        a.resize(n, 0), b.resize(n, 0);
        ntt(a), ntt(b);
        for (int i = 0; i < n; i++) a[i] *= b[i];
        intt(a), a.resize(k);
        return a;
    }
};

template <typename T>
int Number_Theoretic_Transform<T>::max_base = 0;

template <typename T>
T Number_Theoretic_Transform<T>::root = T();

template <typename T>
vector<T> Number_Theoretic_Transform<T>::r = vector<T>();

template <typename T>
vector<T> Number_Theoretic_Transform<T>::ir = vector<T>();

using NTT = Number_Theoretic_Transform<mint>;

vector<mint> convolve(vector<mint> a, vector<mint> b) {
    int n = sz(a), m = sz(b);
    vector<mint> c(n + m - 1, 0);
    rep(i, n) rep(j, m) c[i + j] += a[i] * b[j];
    return c;
}

void solve() {
    int N, M, K;
    cin >> N >> M >> K;

    vector<mint> f(2 * M + 1, 0);
    rep2(i, -M, M + 1) {
        if (abs(i) != K) f[M + i]++;
    }
    // print(f);

    int D = 1000;

    vector<vector<mint>> g(D + 1);
    g[0] = {1};
    rep(i, D) g[i + 1] = convolve(g[i], f);

    auto f_D = g[D];
    f_D.resize(1 << 19, 0);
    NTT::ntt(f_D);

    int L = ceil(N, D);
    vector<vector<mint>> h(L + 1, vector<mint>(1 << 19, 1));
    rep(i, L) rep(j, 1 << 19) h[i + 1][j] = h[i][j] * f_D[j];
    rep(i, L + 1) NTT::intt(h[i]);

    auto calc = [&](int i) {
        int j = i / D, k = i % D;
        mint ret = 0;
        rep(l, sz(g[k])) {
            if (M * i - l < 0) break;
            ret += g[k][l] * h[j][M * i - l];
        }
        return ret;
    };

    vector<mint> c(N + 1, 0);
    rep(i, N + 1) c[i] = calc(i);
    // print(c);

    mint ans = 0;
    mint tw = mint(2).inverse();
    rep2(i, 1, N + 1) {
        mint x = mint(2 * M + 1 - (K == 0 ? 1 : 2)).pow(i) - c[i];
        // cout << i MM mint(2 * M + 1 - (K == 0 ? 1 : 2)).pow(i) MM c[i] << '\n';
        x *= tw;
        x *= mint(2 * M + 1 - (K == 0 ? 1 : 2)).pow(N - i);
        // cout << i MM x << '\n';
        ans += x;
        ans += x * (N - i);
    }

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

int main() {
    int T = 1;
    // cin >> T;
    while (T--) solve();
}
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