結果
問題 | No.8046 yukicoderの過去問 |
ユーザー | risujiroh |
提出日時 | 2019-04-02 05:52:05 |
言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
結果 |
WA
|
実行時間 | - |
コード長 | 7,097 bytes |
コンパイル時間 | 2,023 ms |
コンパイル使用メモリ | 180,796 KB |
実行使用メモリ | 10,136 KB |
最終ジャッジ日時 | 2024-11-27 19:38:00 |
合計ジャッジ時間 | 5,787 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge2 |
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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 | 3 ms
5,248 KB |
testcase_01 | AC | 3 ms
5,248 KB |
testcase_02 | AC | 2 ms
5,248 KB |
testcase_03 | WA | - |
testcase_04 | AC | 2 ms
5,248 KB |
testcase_05 | AC | 793 ms
10,136 KB |
testcase_06 | WA | - |
testcase_07 | WA | - |
testcase_08 | WA | - |
ソースコード
#include <bits/stdc++.h> using namespace std; using lint = long long; template<class T = int> using V = vector<T>; template<class T = int> using VV = V< V<T> >; template<unsigned P> struct ModInt { using M = ModInt; unsigned v; ModInt() : v(0) {} template<class Z> ModInt(Z x) : v(x >= 0 ? x % P : (P - -x % P) % P) {} constexpr ModInt(unsigned v, int) : v(v) {} static constexpr unsigned p() { return P; } M operator+() const { return *this; } M operator-() const { return {v ? P - v : 0, 0}; } explicit operator bool() const noexcept { return v; } bool operator!() const noexcept { return !(bool) *this; } M operator*(M r) const { return M(*this) *= r; } M operator/(M r) const { return M(*this) /= r; } M operator+(M r) const { return M(*this) += r; } M operator-(M r) const { return M(*this) -= r; } bool operator==(M r) const { return v == r.v; } bool operator!=(M r) const { return !(*this == r); } M& operator*=(M r) { v = (uint64_t) v * r.v % P; return *this; } M& operator/=(M r) { return *this *= r.inv(); } M& operator+=(M r) { if ((v += r.v) >= P) v -= P; return *this; } M& operator-=(M r) { if ((v += P - r.v) >= P) v -= P; return *this; } M inv() const { int a = v, b = P, x = 1, u = 0; while (b) { int q = a / b; swap(a -= q * b, b); swap(x -= q * u, u); } assert(a == 1); return x; } template<class Z> M pow(Z n) const { if (n < 0) return pow(-n).inv(); M res = 1; for (M a = *this; n; a *= a, n >>= 1) if (n & 1) res *= a; return res; } template<class Z> friend M operator*(Z l, M r) { return M(l) *= r; } template<class Z> friend M operator/(Z l, M r) { return M(l) /= r; } template<class Z> friend M operator+(Z l, M r) { return M(l) += r; } template<class Z> friend M operator-(Z l, M r) { return M(l) -= r; } friend ostream& operator<<(ostream& os, M r) { return os << r.v; } friend istream& operator>>(istream& is, M& r) { lint x; is >> x; r = x; return is; } template<class Z> friend bool operator==(Z l, M r) { return M(l) == r; } template<class Z> friend bool operator!=(Z l, M r) { return !(l == r); } }; template<unsigned P, unsigned g> void ntt(V< ModInt<P> >& a, bool inv = false) { int n = a.size(); int j = 0; for (int i = 1; i < n; ++i) { int k = n >> 1; while (j >= k) j -= k, k >>= 1; j += k; if (i < j) swap(a[i], a[j]); } assert((P - 1) % n == 0); auto xi = ModInt<P>(g).pow((P - 1) / n); if (inv) xi = xi.inv(); for (int k = 1; k < n; k <<= 1) { ModInt<P> dt = xi.pow((n >> 1) / k); for (int i0 = 0; i0 < n; i0 += k << 1) { ModInt<P> t = 1; for (int i = i0; i < i0 + k; ++i) { j = i + k; a[j] *= t, t *= dt; tie(a[i], a[j]) = make_pair(a[i] + a[j], a[i] - a[j]); } } } } template<unsigned P, unsigned g = 6420> void multiply(V< ModInt<P> >& a, V< ModInt<P> > b) { assert(!a.empty() and !b.empty()); int n = 1 << __lg(2 * (a.size() + b.size() - 1) - 1); a.resize(n), b.resize(n); ntt<P, g>(a), ntt<P, g>(b); for (int i = 0; i < n; ++i) a[i] *= b[i]; ntt<P, g>(a, true); auto inv_n = ModInt<P>(n).inv(); for (int i = 0; i < n; ++i) a[i] *= inv_n; } /* lint tmod(lint a, lint p) { return (a %= p) < 0 ? a + p : a; } lint mod_inv(lint a, lint p) { a = tmod(a, p); lint b = p, x = 1, u = 0; while (b) { lint q = a / b; swap(a -= q * b, b); swap(x -= q * u, u); } return a == 1 ? tmod(x, p) : -1; } lint CRT(const V<lint>& a, const V<lint>& p, lint mod) { int n = a.size(); V<lint> y(n); for (int i = 0; i < n; ++i) { y[i] = a[i]; lint prod = 1; for (int j = 0; j < i; ++j) { y[i] -= prod * y[j] % p[i]; (prod *= p[j]) %= p[i]; } y[i] = tmod(y[i], p[i]); for (int j = 0; j < i; ++j) { (y[i] *= mod_inv(p[j], p[i])) %= p[i]; } } lint res = 0, prod = 1; for (int i = 0; i < n; ++i) { res += prod * y[i] % mod; (prod *= p[i]) %= mod; } return res % mod; } void multiply(V<lint>& a, V<lint>& b, lint mod) { using Mint0 = ModInt<469762049>; using Mint1 = ModInt<1811939329>; using Mint2 = ModInt<2013265921>; int n = a.size(), m = b.size(); V<Mint0> a0(n), b0(m); V<Mint1> a1(n), b1(m); V<Mint2> a2(n), b2(m); for (int i = 0; i < n; ++i) { a[i] %= mod; a0[i] = a[i], a1[i] = a[i], a2[i] = a[i]; } for (int j = 0; j < m; ++j) { b[j] %= mod; b0[j] = b[j], b1[j] = b[j], b2[j] = b[j]; } multiply(a0, b0); multiply(a1, b1); multiply(a2, b2); n = a0.size(); a.resize(n); for (int i = 0; i < n; ++i) { a[i] = CRT({a0[i].v, a1[i].v, a2[i].v}, {Mint0::p(), Mint1::p(), Mint2::p()}, mod); } }*/ using Mint = ModInt<998244353>; /* void multiply(V<Mint>& a, const V<Mint>& b) { int n = a.size(), m = b.size(); V<lint> _a(n), _b(m); for (int i = 0; i < n; ++i) _a[i] = a[i].v; for (int j = 0; j < m; ++j) _b[j] = b[j].v; multiply(_a, _b, Mint::p()); n = _a.size(); a.resize(n); for (int i = 0; i < n; ++i) a[i] = _a[i]; }*/ using namespace chrono; auto start_t = steady_clock::now(); template<class T> struct Polynomial { using P = Polynomial; V<T> c; Polynomial(int n = 0) : c(n) {} void shrink() { while (!c.empty() and !c.back()) c.pop_back(); } int size() const { return c.size(); } T& operator[](int i) { return c[i]; } const T& operator[](int i) const { return c[i]; } P operator*(const P& r) const { return P(*this) *= r; } P operator*(const T& r) const { return P(*this) *= r; } P operator/(const P& r) const { return P(*this) /= r; } P operator+(const P& r) const { return P(*this) += r; } P operator-(const P& r) const { return P(*this) -= r; } P& operator*=(const T& r) { for (int i = 0; i < size(); ++i) c[i] *= r; shrink(); return *this; } P& operator*=(const P& r) { multiply(c, r.c), shrink(); return *this; } P& operator/=(const P& r) { return *this *= r.inverse(); } P& operator+=(const P& r) { if (r.size() > size()) c.resize(r.size()); for (int i = 0; i < r.size(); ++i) c[i] += r[i]; shrink(); return *this; } P& operator-=(const P& r) { if (r.size() > size()) c.resize(r.size()); for (int i = 0; i < r.size(); ++i) c[i] -= r[i]; shrink(); return *this; } P inverse(int n) const { assert(!c.empty() and c[0]); if (n == 1) { P res(1); res[0] = 1 / c[0]; return res; } P inv = inverse(n + 1 >> 1); P res = inv * (T) 2 - *this * inv * inv; res.c.resize(n); cerr << "n = " << n << " (l." << __LINE__ << ")\n"; cerr << "Time: " << duration_cast<milliseconds>(steady_clock::now() - start_t).count() << " ms\n"; return res; } }; using P = Polynomial<Mint>; int main() { cin.tie(nullptr); ios::sync_with_stdio(false); int k, n; cin >> k >> n; start_t = steady_clock::now(); P f(1e5 + 1); f[0] = 1; for (int i = 0; i < n; ++i) { int x; cin >> x; f[x] = -1; } f.shrink(); cout << f.inverse(k + 1)[k] << '\n'; cerr << "Time: " << duration_cast<milliseconds>(steady_clock::now() - start_t).count() << " ms\n"; }