結果
問題 | No.2013 Can we meet? |
ユーザー |
👑 ![]() |
提出日時 | 2023-02-17 02:34:32 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
WA
|
実行時間 | - |
コード長 | 20,217 bytes |
コンパイル時間 | 3,386 ms |
コンパイル使用メモリ | 274,080 KB |
実行使用メモリ | 13,996 KB |
最終ジャッジ日時 | 2024-07-19 01:06:41 |
合計ジャッジ時間 | 7,079 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 WA * 1 |
other | AC * 33 WA * 2 |
ソースコード
#include <bits/stdc++.h>using namespace std;#define FOR(i,m,n) for(int i=(m);i<(n);++i)#define REP(i,n) FOR(i,0,n)#define ALL(v) (v).begin(),(v).end()using ll = long long;constexpr int INF = 0x3f3f3f3f;constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;constexpr double EPS = 1e-8;constexpr int MOD = 998244353;// constexpr int MOD = 1000000007;constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};template <typename T, typename U>inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }template <typename T, typename U>inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }struct IOSetup {IOSetup() {std::cin.tie(nullptr);std::ios_base::sync_with_stdio(false);std::cout << fixed << setprecision(20);}} iosetup;template <int M>struct MInt {unsigned int v;MInt() : v(0) {}MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}static constexpr int get_mod() { return M; }static void set_mod(const int divisor) { assert(divisor == M); }static void init(const int x) {inv<true>(x);fact(x);fact_inv(x);}template <bool MEMOIZES = false>static MInt inv(const int n) {// assert(0 <= n && n < M && std::gcd(n, M) == 1);static std::vector<MInt> inverse{0, 1};const int prev = inverse.size();if (n < prev) return inverse[n];if constexpr (MEMOIZES) {// "n!" and "M" must be disjoint.inverse.resize(n + 1);for (int i = prev; i <= n; ++i) {inverse[i] = -inverse[M % i] * (M / i);}return inverse[n];}int u = 1, v = 0;for (unsigned int a = n, b = M; b;) {const unsigned int q = a / b;std::swap(a -= q * b, b);std::swap(u -= q * v, v);}return u;}static MInt fact(const int n) {static std::vector<MInt> factorial{1};const int prev = factorial.size();if (n >= prev) {factorial.resize(n + 1);for (int i = prev; i <= n; ++i) {factorial[i] = factorial[i - 1] * i;}}return factorial[n];}static MInt fact_inv(const int n) {static std::vector<MInt> f_inv{1};const int prev = f_inv.size();if (n >= prev) {f_inv.resize(n + 1);f_inv[n] = inv(fact(n).v);for (int i = n; i > prev; --i) {f_inv[i - 1] = f_inv[i] * i;}}return f_inv[n];}static MInt nCk(const int n, const int k) {if (n < 0 || n < k || k < 0) return 0;return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :fact_inv(n - k) * fact_inv(k));}static MInt nPk(const int n, const int k) {return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k);}static MInt nHk(const int n, const int k) {return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k));}static MInt large_nCk(long long n, const int k) {if (n < 0 || n < k || k < 0) return 0;inv<true>(k);MInt res = 1;for (int i = 1; i <= k; ++i) {res *= inv(i) * n--;}return res;}MInt pow(long long exponent) const {MInt res = 1, tmp = *this;for (; exponent > 0; exponent >>= 1) {if (exponent & 1) res *= tmp;tmp *= tmp;}return res;}MInt& operator+=(const MInt& x) {if (std::cmp_greater_equal(v += x.v, M)) v -= M;return *this;}MInt& operator-=(const MInt& x) {if (std::cmp_greater_equal(v += M - x.v, M)) v -= M;return *this;}MInt& operator*=(const MInt& x) {v = static_cast<unsigned long long>(v) * x.v % M;return *this;}MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }auto operator<=>(const MInt& x) const = default;MInt& operator++() {if (std::cmp_equal(++v, M)) v = 0;return *this;}MInt operator++(int) {const MInt res = *this;++*this;return res;}MInt& operator--() {v = (v == 0 ? M - 1 : v - 1);return *this;}MInt operator--(int) {const MInt res = *this;--*this;return res;}MInt operator+() const { return *this; }MInt operator-() const { return MInt(v ? M - v : 0); }MInt operator+(const MInt& x) const { return MInt(*this) += x; }MInt operator-(const MInt& x) const { return MInt(*this) -= x; }MInt operator*(const MInt& x) const { return MInt(*this) *= x; }MInt operator/(const MInt& x) const { return MInt(*this) /= x; }friend std::ostream& operator<<(std::ostream& os, const MInt& x) {return os << x.v;}friend std::istream& operator>>(std::istream& is, MInt& x) {long long v;is >> v;x = MInt(v);return is;}};using ModInt = MInt<MOD>;template <int T>struct NumberTheoreticTransform {using ModInt = MInt<T>;NumberTheoreticTransform() {for (int i = 0; i < 23; ++i) {if (primes[i][0] == ModInt::get_mod()) [[unlikely]] {n_max = 1 << primes[i][2];root = ModInt(primes[i][1]).pow((primes[i][0] - 1) >> primes[i][2]);return;}}assert(false);}template <typename U>std::vector<ModInt> dft(const std::vector<U>& a) {std::vector<ModInt> b(std::bit_ceil(a.size()), 0);std::copy(a.begin(), a.end(), b.begin());calc(&b);return b;}void idft(std::vector<ModInt>* a) {assert(std::has_single_bit(a->size()));calc(a);std::reverse(std::next(a->begin()), a->end());const int n = a->size();const ModInt inv_n = ModInt::inv(n);for (int i = 0; i < n; ++i) {(*a)[i] *= inv_n;}}template <typename U>std::vector<ModInt> convolution(const std::vector<U>& a,const std::vector<U>& b) {const int a_size = a.size(), b_size = b.size();const int c_size = a_size + b_size - 1;const int n = std::bit_ceil(static_cast<unsigned int>(c_size));std::vector<ModInt> c(n, 0), d(n, 0);std::copy(a.begin(), a.end(), c.begin());calc(&c);std::copy(b.begin(), b.end(), d.begin());calc(&d);for (int i = 0; i < n; ++i) {c[i] *= d[i];}idft(&c);c.resize(c_size);return c;}private:const int primes[23][3]{{16957441, 329, 14},{17006593, 26, 15},{19529729, 770, 17},{167772161, 3, 25},{469762049, 3, 26},{645922817, 3, 23},{897581057, 3, 23},{924844033, 5, 21},{935329793, 3, 22},{943718401, 7, 22},{950009857, 7, 21},{962592769, 7, 21},{975175681, 17, 21},{976224257, 3, 20},{985661441, 3, 22},{998244353, 3, 23},{1004535809, 3, 21},{1007681537, 3, 20},{1012924417, 5, 21},{1045430273, 3, 20},{1051721729, 6, 20},{1053818881, 7, 20},{1224736769, 3, 24}};int n_max;ModInt root;std::vector<int> butterfly{0};std::vector<std::vector<ModInt>> omega{{1}};void calc(std::vector<ModInt>* a) {const int n = a->size(), prev_n = butterfly.size();if (n > prev_n) {assert(n <= n_max);butterfly.resize(n);const int prev_lg = omega.size(), lg = std::countr_zero(a->size());for (int i = 1; i < prev_n; ++i) {butterfly[i] <<= lg - prev_lg;}for (int i = prev_n; i < n; ++i) {butterfly[i] = (butterfly[i >> 1] >> 1) | ((i & 1) << (lg - 1));}omega.resize(lg);for (int i = prev_lg; i < lg; ++i) {omega[i].resize(1 << i);const ModInt tmp = root.pow((ModInt::get_mod() - 1) >> (i + 1));for (int j = 0; j < (1 << (i - 1)); ++j) {omega[i][j << 1] = omega[i - 1][j];omega[i][(j << 1) + 1] = omega[i - 1][j] * tmp;}}}const int shift =std::countr_zero(butterfly.size()) - std::countr_zero(a->size());for (int i = 0; i < n; ++i) {const int j = butterfly[i] >> shift;if (i < j) std::swap((*a)[i], (*a)[j]);}for (int block = 1, den = 0; block < n; block <<= 1, ++den) {for (int i = 0; i < n; i += (block << 1)) {for (int j = 0; j < block; ++j) {const ModInt tmp = (*a)[i + j + block] * omega[den][j];(*a)[i + j + block] = (*a)[i + j] - tmp;(*a)[i + j] += tmp;}}}}};template <typename T>struct FormalPowerSeries {std::vector<T> coef;explicit FormalPowerSeries(const int deg = 0) : coef(deg + 1, 0) {}explicit FormalPowerSeries(const std::vector<T>& coef) : coef(coef) {}FormalPowerSeries(const std::initializer_list<T> init): coef(init.begin(), init.end()) {}template <typename InputIter>explicit FormalPowerSeries(const InputIter first, const InputIter last): coef(first, last) {}inline const T& operator[](const int term) const { return coef[term]; }inline T& operator[](const int term) { return coef[term]; }using Mult = std::function<std::vector<T>(const std::vector<T>&,const std::vector<T>&)>;using Sqrt = std::function<bool(const T&, T*)>;static void set_mult(const Mult mult) { get_mult() = mult; }static void set_sqrt(const Sqrt sqrt) { get_sqrt() = sqrt; }void resize(const int deg) { coef.resize(deg + 1, 0); }void shrink() {while (coef.size() > 1 && coef.back() == 0) coef.pop_back();}int degree() const { return std::ssize(coef) - 1; }FormalPowerSeries& operator=(const std::vector<T>& coef_) {coef = coef_;return *this;}FormalPowerSeries& operator=(const FormalPowerSeries& x) = default;FormalPowerSeries& operator+=(const FormalPowerSeries& x) {const int deg_x = x.degree();if (deg_x > degree()) resize(deg_x);for (int i = 0; i <= deg_x; ++i) {coef[i] += x[i];}return *this;}FormalPowerSeries& operator-=(const FormalPowerSeries& x) {const int deg_x = x.degree();if (deg_x > degree()) resize(deg_x);for (int i = 0; i <= deg_x; ++i) {coef[i] -= x[i];}return *this;}FormalPowerSeries& operator*=(const T x) {for (T& e : coef) e *= x;return *this;}FormalPowerSeries& operator*=(const FormalPowerSeries& x) {return *this = get_mult()(coef, x.coef);}FormalPowerSeries& operator/=(const T x) {assert(x != 0);return *this *= static_cast<T>(1) / x;}FormalPowerSeries& operator/=(const FormalPowerSeries& x) {const int n = degree() - x.degree() + 1;if (n <= 0) return *this = FormalPowerSeries();const std::vector<T> tmp = get_mult()(std::vector<T>(coef.rbegin(), std::next(coef.rbegin(), n)),FormalPowerSeries(x.coef.rbegin(),std::next(x.coef.rbegin(), std::min(x.degree() + 1, n))).inv(n - 1).coef);return *this = FormalPowerSeries(std::prev(tmp.rend(), n), tmp.rend());}FormalPowerSeries& operator%=(const FormalPowerSeries& x) {if (x.degree() == 0) return *this = FormalPowerSeries{0};*this -= *this / x * x;resize(x.degree() - 1);return *this;}FormalPowerSeries& operator<<=(const int n) {coef.insert(coef.begin(), n, 0);return *this;}FormalPowerSeries& operator>>=(const int n) {if (degree() < n) return *this = FormalPowerSeries();coef.erase(coef.begin(), coef.begin() + n);return *this;}bool operator==(FormalPowerSeries x) const {x.shrink();FormalPowerSeries y = *this;y.shrink();return x.coef == y.coef;}FormalPowerSeries operator+() const { return *this; }FormalPowerSeries operator-() const {FormalPowerSeries res = *this;for (T& e : res.coef) e = -e;return res;}FormalPowerSeries operator+(const FormalPowerSeries& x) const {return FormalPowerSeries(*this) += x;}FormalPowerSeries operator-(const FormalPowerSeries& x) const {return FormalPowerSeries(*this) -= x;}FormalPowerSeries operator*(const T x) const {return FormalPowerSeries(*this) *= x;}FormalPowerSeries operator*(const FormalPowerSeries& x) const {return FormalPowerSeries(*this) *= x;}FormalPowerSeries operator/(const T x) const {return FormalPowerSeries(*this) /= x;}FormalPowerSeries operator/(const FormalPowerSeries& x) const {return FormalPowerSeries(*this) /= x;}FormalPowerSeries operator%(const FormalPowerSeries& x) const {return FormalPowerSeries(*this) %= x;}FormalPowerSeries operator<<(const int n) const {return FormalPowerSeries(*this) <<= n;}FormalPowerSeries operator>>(const int n) const {return FormalPowerSeries(*this) >>= n;}T horner(const T x) const {T res = 0;for (int i = degree(); i >= 0; --i) {res = res * x + coef[i];}return res;}FormalPowerSeries differential() const {const int deg = degree();assert(deg >= 0);FormalPowerSeries res(std::max(deg - 1, 0));for (int i = 1; i <= deg; ++i) {res[i - 1] = coef[i] * i;}return res;}FormalPowerSeries exp(const int deg) const {assert(coef[0] == 0);const int n = coef.size();const FormalPowerSeries one{1};FormalPowerSeries res = one;for (int i = 1; i <= deg; i <<= 1) {res *= FormalPowerSeries(coef.begin(),std::next(coef.begin(), std::min(n, i << 1)))- res.log((i << 1) - 1) + one;res.coef.resize(i << 1);}res.resize(deg);return res;}FormalPowerSeries exp() const { return exp(degree()); }FormalPowerSeries inv(const int deg) const {assert(coef[0] != 0);const int n = coef.size();FormalPowerSeries res{static_cast<T>(1) / coef[0]};for (int i = 1; i <= deg; i <<= 1) {res = res + res - res * res * FormalPowerSeries(coef.begin(), std::next(coef.begin(), std::min(n, i << 1)));res.coef.resize(i << 1);}res.resize(deg);return res;}FormalPowerSeries inv() const { return inv(degree()); }FormalPowerSeries log(const int deg) const {assert(coef[0] == 1);FormalPowerSeries integrand = differential() * inv(deg - 1);integrand.resize(deg);for (int i = deg; i > 0; --i) {integrand[i] = integrand[i - 1] / i;}integrand[0] = 0;return integrand;}FormalPowerSeries log() const { return log(degree()); }FormalPowerSeries pow(long long exponent, const int deg) const {const int n = coef.size();if (exponent == 0) {FormalPowerSeries res(deg);if (deg != -1) [[unlikely]] res[0] = 1;return res;}assert(deg >= 0);for (int i = 0; i < n; ++i) {if (coef[i] == 0) continue;if (i > deg / exponent) break;const long long shift = exponent * i;T tmp = 1, base = coef[i];for (long long e = exponent; e > 0; e >>= 1) {if (e & 1) tmp *= base;base *= base;}const FormalPowerSeries res = ((*this >> i) / coef[i]).log(deg - shift);return ((res * exponent).exp(deg - shift) * tmp) << shift;}return FormalPowerSeries(deg);}FormalPowerSeries pow(const long long exponent) const {return pow(exponent, degree());}FormalPowerSeries mod_pow(long long exponent,const FormalPowerSeries& md) const {const int deg = md.degree() - 1;if (deg < 0) [[unlikely]] return FormalPowerSeries(-1);const FormalPowerSeries inv_rev_md =FormalPowerSeries(md.coef.rbegin(), md.coef.rend()).inv();const auto mod_mult = [&md, &inv_rev_md, deg](FormalPowerSeries* multiplicand, const FormalPowerSeries& multiplier)-> void {*multiplicand *= multiplier;if (deg < multiplicand->degree()) {const int n = multiplicand->degree() - deg;const FormalPowerSeries quotient =FormalPowerSeries(multiplicand->coef.rbegin(),std::next(multiplicand->coef.rbegin(), n))* FormalPowerSeries(inv_rev_md.coef.begin(),std::next(inv_rev_md.coef.begin(), std::min(deg + 2, n)));*multiplicand -=FormalPowerSeries(std::prev(quotient.coef.rend(), n),quotient.coef.rend()) * md;multiplicand->resize(deg);}multiplicand->shrink();};FormalPowerSeries res{1}, base = *this;for (; exponent > 0; exponent >>= 1) {if (exponent & 1) mod_mult(&res, base);mod_mult(&base, base);}return res;}FormalPowerSeries sqrt(const int deg) const {const int n = coef.size();if (coef[0] == 0) {for (int i = 1; i < n; ++i) {if (coef[i] == 0) continue;if (i & 1) return FormalPowerSeries(-1);const int shift = i >> 1;if (deg < shift) break;FormalPowerSeries res = (*this >> i).sqrt(deg - shift);if (res.coef.empty()) return FormalPowerSeries(-1);res <<= shift;res.resize(deg);return res;}return FormalPowerSeries(deg);}T s;if (!get_sqrt()(coef.front(), &s)) return FormalPowerSeries(-1);FormalPowerSeries res{s};const T half = static_cast<T>(1) / 2;for (int i = 1; i <= deg; i <<= 1) {res = (FormalPowerSeries(coef.begin(),std::next(coef.begin(), std::min(n, i << 1)))* res.inv((i << 1) - 1) + res) * half;}res.resize(deg);return res;}FormalPowerSeries sqrt() const { return sqrt(degree()); }FormalPowerSeries translate(const T c) const {const int n = coef.size();std::vector<T> fact(n, 1), inv_fact(n, 1);for (int i = 1; i < n; ++i) {fact[i] = fact[i - 1] * i;}inv_fact[n - 1] = static_cast<T>(1) / fact[n - 1];for (int i = n - 1; i > 0; --i) {inv_fact[i - 1] = inv_fact[i] * i;}std::vector<T> g(n), ex(n);for (int i = 0; i < n; ++i) {g[i] = coef[i] * fact[i];}std::reverse(g.begin(), g.end());T pow_c = 1;for (int i = 0; i < n; ++i) {ex[i] = pow_c * inv_fact[i];pow_c *= c;}const std::vector<T> conv = get_mult()(g, ex);FormalPowerSeries res(n - 1);for (int i = 0; i < n; ++i) {res[i] = conv[n - 1 - i] * inv_fact[i];}return res;}private:static Mult& get_mult() {static Mult mult = [](const std::vector<T>& a, const std::vector<T>& b)-> std::vector<T> {const int n = a.size(), m = b.size();std::vector<T> res(n + m - 1, 0);for (int i = 0; i < n; ++i) {for (int j = 0; j < m; ++j) {res[i + j] += a[i] * b[j];}}return res;};return mult;}static Sqrt& get_sqrt() {static Sqrt sqrt = [](const T&, T*) -> bool { return false; };return sqrt;}};int main() {FormalPowerSeries<ModInt>::set_mult([](const vector<ModInt>& a, const vector<ModInt>& b) -> vector<ModInt> {static NumberTheoreticTransform<MOD> ntt;return ntt.convolution(a, b);});int n, x1, y1, x2, y2, A, B; cin >> n >> x1 >> y1 >> x2 >> y2 >> A >> B;x2 = abs(x2 - x1);y2 = abs(y2 - y1);if ((x2 + y2) % 2 == 1 || x2 + y2 > n) {cout << 0 << '\n';return 0;}vector<int> a(n); REP(i, n) cin >> a[i];const ModInt al = ModInt::inv(2) * A / (A + B), be = ModInt::inv(2) * B / (A + B);FormalPowerSeries<ModInt> qx(n), qy(n);REP(i, n + 1) qx[i] = al.pow(x2 + i * 2) * ModInt::fact_inv(x2 + i) * ModInt::fact_inv(i);REP(i, n + 1) qy[i] = be.pow(y2 + i * 2) * ModInt::fact_inv(y2 + i) * ModInt::fact_inv(i);qx *= qy;FormalPowerSeries<ModInt> q(n);for (int i = x2 + y2; i <= n * 2; i += 2) {q[i / 2] = qx[(i - x2 - y2) / 2] * ModInt::fact(i);}// REP(i, n + 1) cout << q[i] << " \n"[i == n];qx.resize(n);REP(i, n + 1) qx[i] = al.pow(i * 2) * ModInt::fact_inv(i) * ModInt::fact_inv(i);REP(i, n + 1) qy[i] = be.pow(i * 2) * ModInt::fact_inv(i) * ModInt::fact_inv(i);qx *= qy;FormalPowerSeries<ModInt> s(n);for (int i = 0; i <= n * 2; i += 2) {s[i / 2] = qx[i / 2] * ModInt::fact(i);}q *= s.inv();ModInt ans = 0;FOR(i, 1, n + 1) ans += q[i] * a[i - 1];cout << ans << '\n';return 0;}