#915560 (C++17) No.2484 Add to Variables

• 問題: No.2484 Add to Variables
• ユーザー: KKT89
• 提出日時: 2023-09-23 17:40:15
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 171 ms / 2,000 ms
• コード長: 12,967 bytes
• コンパイル時間: 3,083 ms
• コンパイル使用メモリ: 228,024 KB
• 最終ジャッジ日時: 2025-02-17 01:46:35
• ジャッジサーバーID （参考情報）: judge3 / judge3

ファイルパターン	結果
sample	AC * 4
other	AC * 39

ソースコード

#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
ll myRand(ll B) {
    return (ull)rng() % B;
}
inline double time() {
    return static_cast<long double>(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count()) * 1e-9;
}

template <int mod>
struct static_modint {
    using mint = static_modint;
    int x;

    static_modint() : x(0) {}
    static_modint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    mint& operator+=(const mint& rhs) {
        if ((x += rhs.x) >= mod) x -= mod;
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        if ((x += mod - rhs.x) >= mod) x -= mod;
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        x = (int) (1LL * x * rhs.x % mod);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint pow(long long n) const {
        mint _x = *this, r = 1;
        while (n) {
            if (n & 1) r *= _x;
            _x *= _x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const { return pow(mod - 2); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs.x == rhs.x;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs.x != rhs.x;
    }

    friend ostream &operator<<(ostream &os, const mint &p) {
        return os << p.x;
    }
    friend istream &operator>>(istream &is, mint &a) {
        int64_t t; is >> t;
        a = static_modint<mod>(t);
        return (is);
    }
};

const unsigned int mod = 998244353;
using modint = static_modint<mod>;
modint mod_pow(ll n, ll x) { return modint(n).pow(x); }
modint mod_pow(modint n, ll x) { return n.pow(x); }

template <typename T>
struct Comination {
    vector<T> p, invp;

    Comination(int sz) : p(sz+1), invp(sz+1) {
        p[0] = 1;
        for (int i = 1; i <= sz; ++i) {
            p[i] = p[i-1] * i;
        }
        invp[sz] = p[sz].inv();
        for (int i = sz-1; i >= 0; --i) {
            invp[i] = invp[i+1] * (i+1);
        }
    }

    T comb(int n, int r) {
        if (r < 0 or n < r) return 0;
        return p[n]*invp[n-r]*invp[r];
    }
    T big_comb(T n, int r) {
        T res = invp[r];
        for (int i = 0; i < r; ++i) {
            res *= (n-i);
        }
        return res;
    }
};
using Comb = Comination<modint>;
Comb p(1<<20);

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

constexpr int countr_zero_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

struct fft_info {
    int g;
    static constexpr int rank2 = countr_zero_constexpr(mod - 1);
    std::array<modint, rank2 + 1> root;   // root[i]^(2^i) == 1
    std::array<modint, rank2 + 1> iroot;  // root[i] * iroot[i] == 1

    std::array<modint, std::max(0, rank2 - 2 + 1)> rate2;
    std::array<modint, std::max(0, rank2 - 2 + 1)> irate2;

    std::array<modint, std::max(0, rank2 - 3 + 1)> rate3;
    std::array<modint, std::max(0, rank2 - 3 + 1)> irate3;

    fft_info() {
        g = primitive_root<mod>;
        root[rank2] = (mod_pow(g, (mod - 1) >> rank2));
        iroot[rank2] = root[rank2].inv();
        for (int i = rank2 - 1; i >= 0; i--) {
            root[i] = root[i + 1] * root[i + 1];
            iroot[i] = iroot[i + 1] * iroot[i + 1];
        }

        {
            modint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 2; i++) {
                rate2[i] = root[i + 2] * prod;
                irate2[i] = iroot[i + 2] * iprod;
                prod *= iroot[i + 2];
                iprod *= root[i + 2];
            }
        }
        {
            modint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 3; i++) {
                rate3[i] = root[i + 3] * prod;
                irate3[i] = iroot[i + 3] * iprod;
                prod *= iroot[i + 3];
                iprod *= root[i + 3];
            }
        }
    }
};

void butterfly(vector<modint> &a) {
    int n = int(a.size());
    int h = __builtin_ctz(n);

    static const fft_info info;
    int len = 0;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while (len < h) {
        if (h - len == 1) {
            int pp = 1 << (h - len - 1);
            modint rot = 1;
            for (int s = 0; s < (1 << len); s++) {
                int offset = s << (h - len);
                for (int i = 0; i < pp; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + pp] * rot;
                    a[i + offset] = l + r;
                    a[i + offset + pp] = l - r;
                }
                if (s + 1 != (1 << len))
                    rot *= info.rate2[__builtin_ctz(~(unsigned int)(s))];
            }
            len++;
        } else {
            // 4-base
            int pp = 1 << (h - len - 2);
            modint rot = 1, imag = info.root[2];
            for (int s = 0; s < (1 << len); s++) {
                modint rot2 = rot * rot;
                modint rot3 = rot2 * rot;
                int offset = s << (h - len);
                for (int i = 0; i < pp; i++) {
                    auto mod2 = 1ULL * mod * mod;
                    auto a0 = 1ULL * a[i + offset].x;
                    auto a1 = 1ULL * a[i + offset + pp].x * rot.x;
                    auto a2 = 1ULL * a[i + offset + 2 * pp].x * rot2.x;
                    auto a3 = 1ULL * a[i + offset + 3 * pp].x * rot3.x;
                    auto a1na3imag =
                            1ULL * modint(a1 + mod2 - a3).x * imag.x;
                    auto na2 = mod2 - a2;
                    a[i + offset] = a0 + a2 + a1 + a3;
                    a[i + offset + 1 * pp] = a0 + a2 + (2 * mod2 - (a1 + a3));
                    a[i + offset + 2 * pp] = a0 + na2 + a1na3imag;
                    a[i + offset + 3 * pp] = a0 + na2 + (mod2 - a1na3imag);
                }
                if (s + 1 != (1 << len))
                    rot *= info.rate3[__builtin_ctz(~(unsigned int)(s))];
            }
            len += 2;
        }
    }
}

void butterfly_inv(vector<modint> &a) {
    int n = int(a.size());
    int h = __builtin_ctz(n);

    static const fft_info info;
    int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while (len) {
        if (len == 1) {
            int pp = 1 << (h - len);
            modint irot = 1;
            for (int s = 0; s < (1 << (len - 1)); s++) {
                int offset = s << (h - len + 1);
                for (int i = 0; i < pp; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + pp];
                    a[i + offset] = l + r;
                    a[i + offset + pp] =
                            (unsigned long long)(mod + l.x - r.x) *
                            irot.x;
                }
                if (s + 1 != (1 << (len - 1)))
                    irot *= info.irate2[__builtin_ctz(~(unsigned int)(s))];
            }
            len--;
        } else {
            // 4-base
            int pp = 1 << (h - len);
            modint irot = 1, iimag = info.iroot[2];
            for (int s = 0; s < (1 << (len - 2)); s++) {
                modint irot2 = irot * irot;
                modint irot3 = irot2 * irot;
                int offset = s << (h - len + 2);
                for (int i = 0; i < pp; i++) {
                    auto a0 = 1ULL * a[i + offset + 0 * pp].x;
                    auto a1 = 1ULL * a[i + offset + 1 * pp].x;
                    auto a2 = 1ULL * a[i + offset + 2 * pp].x;
                    auto a3 = 1ULL * a[i + offset + 3 * pp].x;

                    auto a2na3iimag = 1ULL * modint((mod + a2 - a3) * iimag.x).x;

                    a[i + offset] = a0 + a1 + a2 + a3;
                    a[i + offset + 1 * pp] =
                            (a0 + (mod - a1) + a2na3iimag) * irot.x;
                    a[i + offset + 2 * pp] =
                            (a0 + a1 + (mod - a2) + (mod - a3)) *
                            irot2.x;
                    a[i + offset + 3 * pp] =
                            (a0 + (mod - a1) + (mod - a2na3iimag)) *
                            irot3.x;
                }
                if (s + 1 != (1 << (len - 2)))
                    irot *= info.irate3[__builtin_ctz(~(unsigned int)(s))];
            }
            len -= 2;
        }
    }
}

vector<modint> convolution_naive(const vector<modint>& a, const vector<modint>& b) {
    int n = int(a.size()), m = int(b.size());
    vector<modint> res(n + m - 1);
    if (n < m) {
        for (int j = 0; j < m; ++j) {
            for (int i = 0; i < n; ++i) {
                res[i + j] += a[i] * b[j];
            }
        }
    } else {
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < m; ++j) {
                res[i + j] += a[i] * b[j];
            }
        }
    }
    return res;
}

vector<modint> convolution_fft(vector<modint>& a, vector<modint>& b) {
    int n = int(a.size()), m = int(b.size());
    int z = 1;
    while (z < n + m - 1) z *= 2;
    a.resize(z);
    butterfly(a);
    b.resize(z);
    butterfly(b);
    for (int i = 0; i < z; ++i) {
        a[i] *= b[i];
    }
    butterfly_inv(a);
    a.resize(n + m - 1);
    modint iz = modint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
    return a;
}

template <class T>
vector<T> convolution(const vector<T>& a, const vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n or !m) return {};

    int z = 1;
    while (z < n + m - 1) z *= 2;
    assert((mod - 1) % z == 0);

    vector<modint> a2(n), b2(m);
    for (int i = 0; i < n; ++i) {
        a2[i] = modint(a[i]);
    }
    for (int i = 0; i < m; ++i) {
        b2[i] = modint(b[i]);
    }

    vector<T> c(n + m - 1);
    vector<modint> c2;

    if (min(n,m) <= 60) c2 = convolution_naive(a2, b2);
    else c2 = convolution_fft(a2, b2);

    for (int i = 0; i < n + m - 1; ++i) {
        c[i] = c2[i].x;
    }
    return c;
}

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int n,m; cin >> n >> m;
    vector<int> b(n);
    for (int i = 0; i < n; ++i) {
        cin >> b[i];
    }
    vector<int> a(n-1);
    int l = 0, r = 0;
    for (int i = 1; i < n; ++i) {
        a[i-1] = b[i] - b[i-1];
        if (a[i-1] < 0) l += abs(a[i-1]);
        else r += a[i-1];
    }

    vector<modint> dp(m+1); dp[0] = 1;
    for (int dif : a) {
        vector<modint> f(m+1);
        for (int i = abs(dif); i <= m; i += 2) {
            int j = (i-abs(dif))/2;
            f[i] = p.invp[j] * p.invp[abs(dif)+j];
        }
        auto ndp = convolution(dp, f);
        swap(dp, ndp);
        while (dp.size() > m+1) dp.pop_back();
    }


    modint res = 0;
    for (int i = 0; i <= m; ++i) {
        if (i > b[0]+b.back()) break;
        int al = b[0]+b.back()-i;
        if (al < 0) continue;
        int L = b[0]-al, R = b.back()-al;
        if (l > L or r > R) continue;
        res += dp[L+R] * p.invp[al] * p.invp[m-i];
    }
    cout << res*p.p[m] << endl;
}