結果
| 問題 | No.1533 Don't be Negative! |
| ユーザー |
👑  tatyam
|
| 提出日時 | 2021-05-28 02:49:04 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 434 ms / 8,000 ms |
| コード長 | 10,269 bytes |
| コンパイル時間 | 3,174 ms |
| コンパイル使用メモリ | 219,312 KB |
| 最終ジャッジ日時 | 2025-01-21 18:52:02 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 53 |
ソースコード
#include <bits/stdc++.h>using namespace std;#ifdef DEBUGint __lg(int n){ return 31 - __builtin_clz(n); }#endiftemplate <class T> vector<T> operator-(vector<T> a) {for (auto&& e : a) e = -e;return a;}template <class T> vector<T>& operator+=(vector<T>& a, const vector<T>& b) {a.resize(max(a.size(), b.size()));for (int i = 0; i < (int)b.size(); ++i) a[i] += b[i];return a;}template <class T> vector<T> operator+(vector<T> a, const vector<T>& b) {return a += b;}template <class T> vector<T>& operator-=(vector<T>& a, const vector<T>& b) {a.resize(max(a.size(), b.size()));for (int i = 0; i < (int)b.size(); ++i) a[i] -= b[i];return a;}template <class T> vector<T> operator-(vector<T> a, const vector<T>& b) {return a -= b;}template <class T> vector<T>& operator<<=(vector<T>& a, size_t n) {return a.insert(begin(a), n, 0), a;}template <class T> vector<T> operator<<(vector<T> a, size_t n) {return a <<= n;}template <class T> vector<T>& operator>>=(vector<T>& a, size_t n) {return a.erase(begin(a), begin(a) + min(a.size(), n)), a;}template <class T> vector<T> operator>>(vector<T> a, size_t n) {return a >>= n;}template <class T> vector<T> operator*(const vector<T>& a, const vector<T>& b) {if (a.empty() or b.empty()) return {};vector<T> res(a.size() + b.size() - 1);for (int i = 0; i < (int)a.size(); ++i)for (int j = 0; j < (int)b.size(); ++j) res[i + j] += a[i] * b[j];return res;}template <class T> vector<T>& operator*=(vector<T>& a, const vector<T>& b) {return a = a * b;}template <class T> vector<T> inverse(const vector<T>& a) {assert(not a.empty() and not (a[0] == 0));vector<T> b{1 / a[0]};while (b.size() < a.size()) {vector<T> x(begin(a), begin(a) + min(a.size(), 2 * b.size()));x *= b * b;b.resize(2 * b.size());for (auto i = b.size() / 2; i < min(x.size(), b.size()); ++i) b[i] = -x[i];}return {begin(b), begin(b) + a.size()};}template <class T> vector<T> operator/(vector<T> a, vector<T> b) {if (a.size() < b.size()) return {};reverse(begin(a), end(a)), reverse(begin(b), end(b));int n = a.size() - b.size() + 1;a.resize(n), b.resize(n);a *= inverse(b);return {rend(a) - n, rend(a)};}template <class T> vector<T>& operator/=(vector<T>& a, const vector<T>& b) {return a = a / b;}template <class T> vector<T> operator%(vector<T> a, const vector<T>& b) {if (a.size() < b.size()) return a;a -= a / b * b;return {begin(a), begin(a) + (b.size() - 1)};}template <class T> vector<T>& operator%=(vector<T>& a, const vector<T>& b) {return a = a % b;}template <class T> vector<T> derivative(const vector<T>& a) {vector<T> res(max((int)a.size() - 1, 0));for (int i = 0; i < (int)res.size(); ++i) res[i] = (i + 1) * a[i + 1];return res;}template <class T> vector<T> primitive(const vector<T>& a) {vector<T> res(a.size() + 1);for (int i = 1; i < (int)res.size(); ++i) res[i] = a[i - 1] / i;return res;}template <class T> vector<T> logarithm(const vector<T>& a) {assert(not a.empty() and a[0] == 1);auto res = primitive(derivative(a) * inverse(a));return {begin(res), begin(res) + a.size()};}template <class T> vector<T> exponent(const vector<T>& a) {assert(a.empty() or a[0] == 0);vector<T> b{1};while (b.size() < a.size()) {vector<T> x(begin(a), begin(a) + min(a.size(), 2 * b.size()));x[0] += 1;b.resize(2 * b.size());x -= logarithm(b);x *= {begin(b), begin(b) + b.size() / 2};for (auto i = b.size() / 2; i < min(x.size(), b.size()); ++i) b[i] = x[i];}return {begin(b), begin(b) + a.size()};}template <class T, class Op = multiplies<T>>constexpr T power(T a, long long n, Op op = Op(), T e = {1}) {assert(n >= 0);while (n) {if (n & 1) e = op(e, a);if (n >>= 1) a = op(a, a);}return e;}template <class T> void ntt(vector<T>& a, bool inverse) {int n = size(a);assert((n & (n - 1)) == 0);if (n < 2) return;assert((T::mod - 1) % n == 0);static vector<T> w{1}, iw{1};for (int m = size(w); m < n / 2; m *= 2) {static T root = 2;while (power(root, (T::mod - 1) / 2) == 1) root += 1;T dw = power(root, (T::mod - 1) / (4 * m)), idw = 1 / dw;w.resize(2 * m), iw.resize(2 * m);for (int i = 0; i < m; ++i) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * idw;}if (not inverse) {for (int m = n; m >>= 1; ) {for (int s = 0, k = 0; s < n; s += 2 * m, ++k) {for (int i = s, j = s + m; i < s + m; ++i, ++j) {T x = a[i], y = a[j] * w[k];a[i] = x + y, a[j] = x - y;}}}} else {for (int m = 1; m < n; m *= 2) {for (int s = 0, k = 0; s < n; s += 2 * m, ++k) {for (int i = s, j = s + m; i < s + m; ++i, ++j) {T x = a[i], y = a[j];a[i] = x + y, a[j] = (x - y) * iw[k];}}}auto inv = 1 / T(n);for (auto&& e : a) e *= inv;}}template <unsigned M> struct montgomery {using m = montgomery;static constexpr unsigned mod = M, neg_inv = [] {static_assert(mod < 1 << 30 and mod & 1);auto inv = mod;while (mod * inv != 1) inv *= 2 - mod * inv;return -inv;}(), sq = -(uint64_t)mod % mod;static unsigned reduce(uint64_t x) {return (x + (uint64_t)mod * ((unsigned)x * neg_inv)) >> 32;}unsigned v;montgomery() : v(0) {}montgomery(long long x) {if ((x %= mod) < 0) x += mod;v = reduce((uint64_t)x * sq);}int get() const {auto res = reduce(v);return res < mod ? res : res - mod;}m operator-() const { return m() -= *this; }m& operator+=(m b) {if ((int)(v += b.v - 2 * mod) < 0) v += 2 * mod;return *this;}m& operator-=(m b) {if ((int)(v -= b.v) < 0) v += 2 * mod;return *this;}m& operator*=(m b) {v = reduce((uint64_t)v * b.v);return *this;}m& operator/=(m b) { return *this *= power(b, mod - 2); }friend m operator+(m a, m b) { return a += b; }friend m operator-(m a, m b) { return a -= b; }friend m operator*(m a, m b) { return a *= b; }friend m operator/(m a, m b) { return a /= b; }friend bool operator==(m a, m b) { return a.v == b.v; }};using mint = montgomery<998244353>;vector<mint> fact, inv_fact, minv;void prepare(int n) {fact.resize(n + 1), inv_fact.resize(n + 1), minv.resize(n + 1);for (int i = 0; i <= n; ++i) fact[i] = i ? fact[i - 1] * i : 1;inv_fact[n] = power(fact[n], mint::mod - 2);for (int i = n; i--; ) inv_fact[i] = (i + 1) * inv_fact[i + 1];for (int i = 1; i <= n; ++i) minv[i] = inv_fact[i] * fact[i - 1];}mint binom(int n, int k) {if (k < 0 or k > n) return 0;return fact[n] * inv_fact[k] * inv_fact[n - k];}template <> mint& mint::operator/=(mint b) {return *this *= b.v < minv.size() ? minv[b.v] : power(b, mod - 2);}struct dual_vec {vector<mint> v;void resize(int sz) { v.resize(sz); }};dual_vec mfft(const vector<mint>& a, int sz) {dual_vec fa{a};fa.resize(sz), ntt(fa.v, false);return fa;}dual_vec operator*(dual_vec a, const dual_vec& b) {for (int i = 0; i < (int)a.v.size(); ++i) a.v[i] *= b.v[i];return a;}vector<mint> ifft(dual_vec fa, int n) {ntt(fa.v, true), fa.resize(n);return fa.v;}vector<mint> operator*(const vector<mint>& a, const vector<mint>& b) {if (a.empty() or b.empty()) return {};int n = a.size(), m = b.size(), sz = 1 << __lg(2 * (n + m - 1) - 1);if (min(n, m) < 30) {vector<mint> c(n + m - 1);for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j)c[i + j] += a[i] * b[j];return c;}if (a == b) {dual_vec fl = mfft(a, sz);return ifft(fl * fl, n + m - 1);}return ifft(mfft(a, sz) * mfft(b, sz), n + m - 1);}vector<mint> inverse(const vector<mint>& a) {assert(not a.empty() and not (a[0] == 0));vector<mint> b{1 / a[0]};for (int m = 1; m < (int)a.size(); m *= 2) {vector<mint> x(begin(a), begin(a) + min<int>(a.size(), 2 * m));dual_vec fb = mfft(b, 2 * m);x = ifft(mfft(x, 2 * m) * fb, 2 * m);fill(begin(x), begin(x) + m, 0);x = -ifft(mfft(x, 2 * m) * fb, 2 * m);b.insert(end(b), begin(x) + m, end(x));}return {begin(b), begin(b) + a.size()};}vector<mint> exponent(const vector<mint>& a) {assert(a.empty() or a[0] == 0);vector<mint> b{1, 1 < a.size() ? a[1] : 0}, c{1};dual_vec half_fc = mfft(c, 1), fc = mfft(c, 2);for (int m = 2; m < (int)a.size(); m *= 2) {dual_vec fb = mfft(b, 2 * m), half_fb = fb;half_fb.resize(m);half_fc = fc;vector<mint> z = ifft(half_fb * half_fc, m);fill(begin(z), begin(z) + m / 2, 0);z = -ifft(mfft(z, m) * half_fc, m);c.insert(end(c), begin(z) + m / 2, end(z));fc = mfft(c, 2 * m);vector<mint> x(begin(a), begin(a) + min<int>(a.size(), m));x = derivative(x), x.push_back(0);dual_vec fx = mfft(x, m);x = ifft(fx * half_fb, m);x -= derivative(b);x.resize(2 * m);for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = 0;x = ifft(mfft(x, 2 * m) * fc, 2 * m);x = primitive(x), x.pop_back();for (int i = m; i < min<int>(a.size(), 2 * m); ++i) x[i] += a[i];fill(begin(x), begin(x) + m, 0);x = ifft(mfft(x, 2 * m) * fb, 2 * m);b.insert(end(b), begin(x) + m, end(x));}return {begin(b), begin(b) + a.size()};}vector<mint> power(vector<mint> a, long long m) {int n = size(a), tz = 0;while (tz < n and a[tz] == 0) ++tz;if (n == 0 or (tz and m >= (n + tz - 1) / tz)) return vector<mint>(n);a >>= tz;auto a0 = a[0];a *= vector<mint>{1 / a0};a = exponent(logarithm(a) * vector<mint>{m});a *= vector<mint>{power(a0, m)};return a <<= tz * m;}vector<mint> resize(vector<mint> a, int sz) {a.resize(sz);return a;}int main(){int N, M, K;cin >> N >> M >> K;if(M == K) M--;if(M == 0)return puts("0") & 0;vector<mint> F(M * 2 + 1);mint s = 0;for(int i = -M; i <= M; i++) if(i != K && i != -K){F[i + M] = 1;s += 1;}vector<mint> S(M + 1);S[M] = s;auto Q = vector<mint>{1, -1} * (F - S) * (F - S);F.resize(N * M);auto P = power(F, N + 2);Q.resize(N * M);cout << (P * inverse(Q))[M * N - 1].get() << endl;}