結果
問題 | No.2513 Power Eraser |
ユーザー |
|
提出日時 | 2023-10-20 23:32:26 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 1,696 ms / 6,000 ms |
コード長 | 20,636 bytes |
コンパイル時間 | 1,931 ms |
コンパイル使用メモリ | 105,064 KB |
実行使用メモリ | 32,808 KB |
最終ジャッジ日時 | 2024-09-20 23:32:31 |
合計ジャッジ時間 | 52,798 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 39 |
ソースコード
#include<iostream>#include<cassert>#include<atcoder/segtree>using namespace std;#line 2 "modint/montgomery-modint.hpp"template <uint32_t mod>struct LazyMontgomeryModInt {using mint = LazyMontgomeryModInt;using i32 = int32_t;using u32 = uint32_t;using u64 = uint64_t;static constexpr u32 get_r() {u32 ret = mod;for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;return ret;}static constexpr u32 r = get_r();static constexpr u32 n2 = -u64(mod) % mod;static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");static_assert(r * mod == 1, "this code has bugs.");u32 a;constexpr LazyMontgomeryModInt() : a(0) {}constexpr LazyMontgomeryModInt(const int64_t &b): a(reduce(u64(b % mod + mod) * n2)){};static constexpr u32 reduce(const u64 &b) {return (b + u64(u32(b) * u32(-r)) * mod) >> 32;}constexpr mint &operator+=(const mint &b) {if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;return *this;}constexpr mint &operator-=(const mint &b) {if (i32(a -= b.a) < 0) a += 2 * mod;return *this;}constexpr mint &operator*=(const mint &b) {a = reduce(u64(a) * b.a);return *this;}constexpr mint &operator/=(const mint &b) {*this *= b.inverse();return *this;}constexpr mint operator+(const mint &b) const { return mint(*this) += b; }constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }constexpr bool operator==(const mint &b) const {return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);}constexpr bool operator!=(const mint &b) const {return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);}constexpr mint operator-() const { return mint() - mint(*this); }constexpr mint operator+() const { return mint(*this); }constexpr mint pow(u64 n) const {mint ret(1), mul(*this);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}constexpr mint inverse() const {int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;while (y > 0) {t = x / y;x -= t * y, u -= t * v;tmp = x, x = y, y = tmp;tmp = u, u = v, v = tmp;}return mint{u};}friend ostream &operator<<(ostream &os, const mint &b) {return os << b.get();}friend istream &operator>>(istream &is, mint &b) {int64_t t;is >> t;b = LazyMontgomeryModInt<mod>(t);return (is);}constexpr u32 get() const {u32 ret = reduce(a);return ret >= mod ? ret - mod : ret;}static constexpr u32 get_mod() { return mod; }};#line 2 "fps/ntt-friendly-fps.hpp"#line 2 "ntt/ntt.hpp"template <typename mint>struct NTT {static constexpr uint32_t get_pr() {uint32_t _mod = mint::get_mod();using u64 = uint64_t;u64 ds[32] = {};int idx = 0;u64 m = _mod - 1;for (u64 i = 2; i * i <= m; ++i) {if (m % i == 0) {ds[idx++] = i;while (m % i == 0) m /= i;}}if (m != 1) ds[idx++] = m;uint32_t _pr = 2;while (1) {int flg = 1;for (int i = 0; i < idx; ++i) {u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;while (b) {if (b & 1) r = r * a % _mod;a = a * a % _mod;b >>= 1;}if (r == 1) {flg = 0;break;}}if (flg == 1) break;++_pr;}return _pr;};static constexpr uint32_t mod = mint::get_mod();static constexpr uint32_t pr = get_pr();static constexpr int level = __builtin_ctzll(mod - 1);mint dw[level], dy[level];void setwy(int k) {mint w[level], y[level];w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));y[k - 1] = w[k - 1].inverse();for (int i = k - 2; i > 0; --i)w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];for (int i = 3; i < k; ++i) {dw[i] = dw[i - 1] * y[i - 2] * w[i];dy[i] = dy[i - 1] * w[i - 2] * y[i];}}NTT() { setwy(level); }void fft4(vector<mint> &a, int k) {if ((int)a.size() <= 1) return;if (k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}if (k & 1) {int v = 1 << (k - 1);for (int j = 0; j < v; ++j) {mint ajv = a[j + v];a[j + v] = a[j] - ajv;a[j] += ajv;}}int u = 1 << (2 + (k & 1));int v = 1 << (k - 2 - (k & 1));mint one = mint(1);mint imag = dw[1];while (v) {// jh = 0{int j0 = 0;int j1 = v;int j2 = j1 + v;int j3 = j2 + v;for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];mint t0p2 = t0 + t2, t1p3 = t1 + t3;mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;}}// jh >= 1mint ww = one, xx = one * dw[2], wx = one;for (int jh = 4; jh < u;) {ww = xx * xx, wx = ww * xx;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for (; j0 < je; ++j0, ++j2) {mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,t3 = a[j2 + v] * wx;mint t0p2 = t0 + t2, t1p3 = t1 + t3;mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;}xx *= dw[__builtin_ctzll((jh += 4))];}u <<= 2;v >>= 2;}}void ifft4(vector<mint> &a, int k) {if ((int)a.size() <= 1) return;if (k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}int u = 1 << (k - 2);int v = 1;mint one = mint(1);mint imag = dy[1];while (u) {// jh = 0{int j0 = 0;int j1 = v;int j2 = v + v;int j3 = j2 + v;for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;}}// jh >= 1mint ww = one, xx = one * dy[2], yy = one;u <<= 2;for (int jh = 4; jh < u;) {ww = xx * xx, yy = xx * imag;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for (; j0 < je; ++j0, ++j2) {mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;}xx *= dy[__builtin_ctzll(jh += 4)];}u >>= 4;v <<= 2;}if (k & 1) {u = 1 << (k - 1);for (int j = 0; j < u; ++j) {mint ajv = a[j] - a[j + u];a[j] += a[j + u];a[j + u] = ajv;}}}void ntt(vector<mint> &a) {if ((int)a.size() <= 1) return;fft4(a, __builtin_ctz(a.size()));}void intt(vector<mint> &a) {if ((int)a.size() <= 1) return;ifft4(a, __builtin_ctz(a.size()));mint iv = mint(a.size()).inverse();for (auto &x : a) x *= iv;}vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {int l = a.size() + b.size() - 1;if (min<int>(a.size(), b.size()) <= 40) {vector<mint> s(l);for (int i = 0; i < (int)a.size(); ++i)for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];return s;}int k = 2, M = 4;while (M < l) M <<= 1, ++k;setwy(k);vector<mint> s(M);for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];fft4(s, k);if (a.size() == b.size() && a == b) {for (int i = 0; i < M; ++i) s[i] *= s[i];} else {vector<mint> t(M);for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];fft4(t, k);for (int i = 0; i < M; ++i) s[i] *= t[i];}ifft4(s, k);s.resize(l);mint invm = mint(M).inverse();for (int i = 0; i < l; ++i) s[i] *= invm;return s;}void ntt_doubling(vector<mint> &a) {int M = (int)a.size();auto b = a;intt(b);mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;ntt(b);copy(begin(b), end(b), back_inserter(a));}};#line 2 "fps/formal-power-series.hpp"template <typename mint>struct FormalPowerSeries : vector<mint> {using vector<mint>::vector;using FPS = FormalPowerSeries;FPS &operator+=(const FPS &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];return *this;}FPS &operator+=(const mint &r) {if (this->empty()) this->resize(1);(*this)[0] += r;return *this;}FPS &operator-=(const FPS &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];return *this;}FPS &operator-=(const mint &r) {if (this->empty()) this->resize(1);(*this)[0] -= r;return *this;}FPS &operator*=(const mint &v) {for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;return *this;}FPS &operator/=(const FPS &r) {if (this->size() < r.size()) {this->clear();return *this;}int n = this->size() - r.size() + 1;if ((int)r.size() <= 64) {FPS f(*this), g(r);g.shrink();mint coeff = g.back().inverse();for (auto &x : g) x *= coeff;int deg = (int)f.size() - (int)g.size() + 1;int gs = g.size();FPS quo(deg);for (int i = deg - 1; i >= 0; i--) {quo[i] = f[i + gs - 1];for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];}*this = quo * coeff;this->resize(n, mint(0));return *this;}return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();}FPS &operator%=(const FPS &r) {*this -= *this / r * r;shrink();return *this;}FPS operator+(const FPS &r) const { return FPS(*this) += r; }FPS operator+(const mint &v) const { return FPS(*this) += v; }FPS operator-(const FPS &r) const { return FPS(*this) -= r; }FPS operator-(const mint &v) const { return FPS(*this) -= v; }FPS operator*(const FPS &r) const { return FPS(*this) *= r; }FPS operator*(const mint &v) const { return FPS(*this) *= v; }FPS operator/(const FPS &r) const { return FPS(*this) /= r; }FPS operator%(const FPS &r) const { return FPS(*this) %= r; }FPS operator-() const {FPS ret(this->size());for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];return ret;}void shrink() {while (this->size() && this->back() == mint(0)) this->pop_back();}FPS rev() const {FPS ret(*this);reverse(begin(ret), end(ret));return ret;}FPS dot(FPS r) const {FPS ret(min(this->size(), r.size()));for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];return ret;}// 蜑・sz 鬆・r蜿悶▲縺ヲ縺上k縲Tz 縺ォ雜ウ繧翫↑縺・・・ 0 蝓九a縺吶kFPS pre(int sz) const {FPS ret(begin(*this), begin(*this) + min((int)this->size(), sz));if ((int)ret.size() < sz) ret.resize(sz);return ret;}FPS operator>>(int sz) const {if ((int)this->size() <= sz) return {};FPS ret(*this);ret.erase(ret.begin(), ret.begin() + sz);return ret;}FPS operator<<(int sz) const {FPS ret(*this);ret.insert(ret.begin(), sz, mint(0));return ret;}FPS diff() const {const int n = (int)this->size();FPS ret(max(0, n - 1));mint one(1), coeff(1);for (int i = 1; i < n; i++) {ret[i - 1] = (*this)[i] * coeff;coeff += one;}return ret;}FPS integral() const {const int n = (int)this->size();FPS ret(n + 1);ret[0] = mint(0);if (n > 0) ret[1] = mint(1);auto mod = mint::get_mod();for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];return ret;}mint eval(mint x) const {mint r = 0, w = 1;for (auto &v : *this) r += w * v, w *= x;return r;}FPS log(int deg = -1) const {assert(!(*this).empty() && (*this)[0] == mint(1));if (deg == -1) deg = (int)this->size();return (this->diff() * this->inv(deg)).pre(deg - 1).integral();}FPS pow(int64_t k, int deg = -1) const {const int n = (int)this->size();if (deg == -1) deg = n;if (k == 0) {FPS ret(deg);if (deg) ret[0] = 1;return ret;}for (int i = 0; i < n; i++) {if ((*this)[i] != mint(0)) {mint rev = mint(1) / (*this)[i];FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);ret *= (*this)[i].pow(k);ret = (ret << (i * k)).pre(deg);if ((int)ret.size() < deg) ret.resize(deg, mint(0));return ret;}if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));}return FPS(deg, mint(0));}static void *ntt_ptr;static void set_fft();FPS &operator*=(const FPS &r);void ntt();void intt();void ntt_doubling();static int ntt_pr();FPS inv(int deg = -1) const;FPS exp(int deg = -1) const;};template <typename mint>void *FormalPowerSeries<mint>::ntt_ptr = nullptr;/*** @brief 螟夐・シ・蠖「蠑冗噪蜀ェ邏壽焚繝ゥ繧、繝悶Λ繝ェ* @docs docs/fps/formal-power-series.md*/#line 5 "fps/ntt-friendly-fps.hpp"template <typename mint>void FormalPowerSeries<mint>::set_fft() {if (!ntt_ptr) ntt_ptr = new NTT<mint>;}template <typename mint>FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(const FormalPowerSeries<mint>& r) {if (this->empty() || r.empty()) {this->clear();return *this;}set_fft();auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this, r);return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());}template <typename mint>void FormalPowerSeries<mint>::ntt() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);}template <typename mint>void FormalPowerSeries<mint>::intt() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);}template <typename mint>void FormalPowerSeries<mint>::ntt_doubling() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);}template <typename mint>int FormalPowerSeries<mint>::ntt_pr() {set_fft();return static_cast<NTT<mint>*>(ntt_ptr)->pr;}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {assert((*this)[0] != mint(0));if (deg == -1) deg = (int)this->size();FormalPowerSeries<mint> res(deg);res[0] = {mint(1) / (*this)[0]};for (int d = 1; d < deg; d <<= 1) {FormalPowerSeries<mint> f(2 * d), g(2 * d);for (int j = 0; j < min((int)this->size(), 2 * d); j++) f[j] = (*this)[j];for (int j = 0; j < d; j++) g[j] = res[j];f.ntt();g.ntt();for (int j = 0; j < 2 * d; j++) f[j] *= g[j];f.intt();for (int j = 0; j < d; j++) f[j] = 0;f.ntt();for (int j = 0; j < 2 * d; j++) f[j] *= g[j];f.intt();for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];}return res.pre(deg);}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {using fps = FormalPowerSeries<mint>;assert((*this).size() == 0 || (*this)[0] == mint(0));if (deg == -1) deg = this->size();fps inv;inv.reserve(deg + 1);inv.push_back(mint(0));inv.push_back(mint(1));auto inplace_integral = [&](fps& F) -> void {const int n = (int)F.size();auto mod = mint::get_mod();while ((int)inv.size() <= n) {int i = inv.size();inv.push_back((-inv[mod % i]) * (mod / i));}F.insert(begin(F), mint(0));for (int i = 1; i <= n; i++) F[i] *= inv[i];};auto inplace_diff = [](fps& F) -> void {if (F.empty()) return;F.erase(begin(F));mint coeff = 1, one = 1;for (int i = 0; i < (int)F.size(); i++) {F[i] *= coeff;coeff += one;}};fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};for (int m = 2; m < deg; m *= 2) {auto y = b;y.resize(2 * m);y.ntt();z1 = z2;fps z(m);for (int i = 0; i < m; ++i) z[i] = y[i] * z1[i];z.intt();fill(begin(z), begin(z) + m / 2, mint(0));z.ntt();for (int i = 0; i < m; ++i) z[i] *= -z1[i];z.intt();c.insert(end(c), begin(z) + m / 2, end(z));z2 = c;z2.resize(2 * m);z2.ntt();fps x(begin(*this), begin(*this) + min<int>(this->size(), m));x.resize(m);inplace_diff(x);x.push_back(mint(0));x.ntt();for (int i = 0; i < m; ++i) x[i] *= y[i];x.intt();x -= b.diff();x.resize(2 * m);for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = mint(0);x.ntt();for (int i = 0; i < 2 * m; ++i) x[i] *= z2[i];x.intt();x.pop_back();inplace_integral(x);for (int i = m; i < min<int>(this->size(), 2 * m); ++i) x[i] += (*this)[i];fill(begin(x), begin(x) + m, mint(0));x.ntt();for (int i = 0; i < 2 * m; ++i) x[i] *= y[i];x.intt();b.insert(end(b), begin(x) + m, end(x));}return fps{begin(b), begin(b) + deg};}/*** @brief NTT mod逕ィFPS繝ゥ繧、繝悶Λ繝ェ* @docs docs/fps/ntt-friendly-fps.md*/#line 4 "fps/fast-multieval.hpp"template <typename mint>vector<mint> FastMultiEval(const FormalPowerSeries<mint> &f,const vector<mint> &xs) {using fps = FormalPowerSeries<mint>;int s = xs.size();int N = 1 << (32 - __builtin_clz((int)xs.size() - 1));if(f.empty() || xs.empty()) return vector<mint>(s, mint(0));vector<FormalPowerSeries<mint>> buf(2 * N);for (int i = 0; i < N; i++) {mint n = mint{i < s ? -xs[i] : mint(0)};buf[i + N] = fps{n + 1, n - 1};}for (int i = N - 1; i > 0; i--) {fps &g(buf[(i << 1) | 0]), &h(buf[(i << 1) | 1]);int n = g.size();int m = n << 1;buf[i].reserve(m);buf[i].resize(n);for (int j = 0; j < n; j++) buf[i][j] = g[j] * h[j] - mint(1);if (i != 1) {buf[i].ntt_doubling();for (int j = 0; j < m; j++) buf[i][j] += j < n ? mint(1) : -mint(1);}}int fs = f.size();fps root = buf[1];root.intt();root.push_back(1);reverse(begin(root), end(root));root = root.inv(fs).rev() * f;root.erase(begin(root), begin(root) + fs - 1);root.resize(N, mint(0));vector<mint> ans(s);auto calc = [&](auto rec, int i, int l, int r, fps g) -> void {if (i >= N) {ans[i - N] = g[0];return;}int len = g.size(), m = (l + r) >> 1;g.ntt();fps tmp = buf[i * 2 + 1];for (int j = 0; j < len; j++) tmp[j] *= g[j];tmp.intt();rec(rec, i * 2 + 0, l, m, fps{begin(tmp) + (len >> 1), end(tmp)});if (m >= s) return;tmp = buf[i * 2 + 0];for (int j = 0; j < len; j++) tmp[j] *= g[j];tmp.intt();rec(rec, i * 2 + 1, m, r, fps{begin(tmp) + (len >> 1), end(tmp)});};calc(calc, 1, 0, N, root);return ans;}/*** @brief Multipoint Evaluation(鬮倬·溷喧迚・*/using mint=LazyMontgomeryModInt<998244353>;using fps=FormalPowerSeries<mint>;int N;mint A[2<<17];fps op(fps a,fps b){return a*b;}fps e(){return(fps){mint(1)};}mint f(int L,int R){if(R-L==1)return mint(1);int mid=(L+R)/2;mint Lv=f(L,mid),Rv=f(mid,R);mint ret=Lv*Rv;vector<fps>init(mid-L);for(int i=0;i<mid-L;i++){init[i]={-A[L+i],mint(1)};}atcoder::segtree<fps,op,e>seg(init);fps ALL=seg.all_prod();vector<mint>vs=FastMultiEval(ALL,vector<mint>(A+mid,A+R));for(mint v:vs)ret*=v;return ret;}int main(){ios::sync_with_stdio(false);cin.tie(nullptr);cin>>N;for(int i=0;i<N;i++){int a;cin>>a;A[i]=mint(a);}mint ret=f(0,N);if((long)N*(N-1)/2%2==1)ret=-ret;cout<<ret<<endl;}