結果
| 問題 |
No.2369 Some Products
|
| コンテスト | |
| ユーザー |
 遭難者
|
| 提出日時 | 2023-06-30 21:45:41 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 19,845 bytes |
| コンパイル時間 | 1,783 ms |
| コンパイル使用メモリ | 158,320 KB |
| 実行使用メモリ | 125,696 KB |
| 最終ジャッジ日時 | 2024-07-07 09:26:04 |
| 合計ジャッジ時間 | 15,328 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | WA * 14 |
ソースコード
#include <iostream>
#include <cmath>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <tuple>
#include <cstdint>
#include <cstdio>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <deque>
#include <unordered_map>
#include <unordered_set>
#include <bitset>
#include <cctype>
#include <climits>
#include <functional>
#include <cassert>
#include <numeric>
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
using ll = long long;
#define vi vector<int>
#define vvi vector<vi>
#define vl vector<ll>
#define pii pair<int, int>
#define pll pair<ll, ll>
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define mod 998244353
using namespace std;
struct mint
{
ll x;
mint(ll x = 0) : x((x + mod) % mod) {}
mint operator-() const { return mint(-x); }
mint operator+=(const mint &a)
{
if ((x += a.x) >= mod)
x -= mod;
return *this;
}
mint &operator++()
{
if (++x == mod)
x = 0;
return *this;
}
mint operator++(int)
{
mint temp = *this;
if (++x == mod)
x = 0;
return temp;
}
mint &operator-=(const mint &a)
{
if ((x -= a.x) < 0)
x += mod;
return *this;
}
mint &operator--()
{
if (--x < 0)
x += mod;
return *this;
}
mint operator--(int)
{
mint temp = *this;
if (--x < 0)
x += mod;
return temp;
}
mint &operator*=(const mint &a)
{
(x *= a.x) %= mod;
return *this;
}
mint operator+(const mint &a) const { return mint(*this) += a; }
mint operator-(const mint &a) const { return mint(*this) -= a; }
mint operator*(const mint &a) const { return mint(*this) *= a; }
mint pow(ll t) const
{
if (!t)
return 1;
mint res = 1, v = *this;
while (t)
{
if (t & 1)
res *= v;
v *= v;
t >>= 1;
}
return res;
}
mint inv() const { return pow(mod - 2); }
mint &operator/=(const mint &a) { return (*this) *= a.inv(); }
mint operator/(const mint &a) const { return mint(*this) /= a; }
bool operator==(const mint &a) const { return x == a.x; }
bool operator!=(const mint &a) const { return x != a.x; }
bool operator<(const mint &a) const { return x < a.x; }
bool operator>(const mint &a) const { return x > a.x; }
friend istream &operator>>(istream &is, mint &a) { return is >> a.x; }
friend ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
};
template <class mint>
struct FPS : vector<mint>
{
using vector<mint>::vector;
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;
}
const int n = this->size() - r.size() + 1;
if ((int)r.size() <= 64)
{
FPS f(*this), g(r);
g.shrink();
mint coeff = g.back().inv();
for (auto &x : g)
x *= coeff;
const int deg = (int)f.size() - (int)g.size() + 1;
const 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;
}
FPS pre(int sz) const
{
return FPS(begin(*this), begin(*this) + min((int)this->size(), sz));
}
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));
const mint one(1);
mint 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);
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)[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))
{
const 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 <class mint>
void *FPS<mint>::ntt_ptr = nullptr;
template <class mint>
struct NTT
{
static constexpr uint32_t pr = 3;
static_assert(mod == 998244353);
static constexpr int level = __builtin_ctzll(mod - 1);
mint dw[level], dy[level];
void setwy(const int k)
{
mint w[level], y[level];
w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
y[k - 1] = w[k - 1].inv();
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, const 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)
{
const 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));
const mint one = mint(1);
const 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++)
{
const mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
const mint t0p2 = t0 + t2, t1p3 = t1 + t3;
const 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 >= 1
mint ww = one, xx = one * dw[2], wx = one;
for (int jh = 4; jh < u;)
{
ww = xx * xx, wx = ww * xx;
int j0 = jh * v;
const int je = j0 + v;
int j2 = je + v;
for (; j0 < je; j0++, j2++)
{
const mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
t3 = a[j2 + v] * wx;
const mint t0p2 = t0 + t2, t1p3 = t1 + t3;
const 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, const 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;
const mint one = mint(1);
const 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++)
{
const mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
const mint t0p1 = t0 + t1, t2p3 = t2 + t3;
const 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 >= 1
mint 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;
const int je = j0 + v;
int j2 = je + v;
for (; j0 < je; j0++, j2++)
{
const mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
const mint t0p1 = t0 + t1, t2p3 = t2 + t3;
const 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()));
const mint iv = mint(a.size()).inv();
for (auto &x : a)
x *= iv;
}
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b)
{
const 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), t(M);
for (int i = 0; i < (int)a.size(); i++)
s[i] = a[i];
for (int i = 0; i < (int)b.size(); i++)
t[i] = b[i];
fft4(s, k);
fft4(t, k);
for (int i = 0; i < M; i++)
s[i] *= t[i];
ifft4(s, k);
s.resize(l);
const mint invm = mint(M).inv();
for (int i = 0; i < l; i++)
s[i] *= invm;
return s;
}
void ntt_doubling(vector<mint> &a)
{
const int M = (int)a.size();
auto b = a;
intt(b);
mint r = 1, zeta = mint(pr).pow((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));
}
};
template <class mint>
void FPS<mint>::set_fft()
{
if (!ntt_ptr)
ntt_ptr = new NTT<mint>;
}
template <class mint>
FPS<mint> &FPS<mint>::operator*=(const FPS<mint> &r)
{
if (this->empty() || r.empty())
{
this->clear();
return *this;
}
set_fft();
const auto ret = static_cast<NTT<mint> *>(ntt_ptr)->multiply(*this, r);
return *this = FPS<mint>(ret.begin(), ret.end());
}
template <class mint>
void FPS<mint>::ntt()
{
set_fft();
static_cast<NTT<mint> *>(ntt_ptr)->ntt(*this);
}
template <class mint>
void FPS<mint>::intt()
{
set_fft();
static_cast<NTT<mint> *>(ntt_ptr)->intt(*this);
}
template <class mint>
void FPS<mint>::ntt_doubling()
{
set_fft();
static_cast<NTT<mint> *>(ntt_ptr)->ntt_doubling(*this);
}
template <class mint>
int FPS<mint>::ntt_pr()
{
set_fft();
return static_cast<NTT<mint> *>(ntt_ptr)->pr;
}
template <class mint>
FPS<mint> FPS<mint>::inv(int deg) const
{
assert((*this)[0] != mint(0));
if (deg == -1)
deg = (int)this->size();
FPS<mint> res(deg);
res[0] = {mint(1) / (*this)[0]};
for (int d = 1; d < deg; d <<= 1)
{
FPS<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 <class mint>
FPS<mint> FPS<mint>::exp(int deg) const
{
using fps = FPS<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();
while ((int)inv.size() <= n)
{
const 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};
}
void solve()
{
int n;
cin >> n;
vector<FPS<mint>> dp(1, FPS<mint>(1));
dp[0][0] = 1;
rep(j, n)
{
auto addition = dp[j];
addition.push_back(0);
int x;
cin >> x;
rep(i, j + 1) addition[i + 1] += x * dp[j][i].x;
dp.push_back(addition);
}
int query;
cin >> query;
rep(loop, query)
{
int l, r, k;
cin >> l >> r >> k;
l--;
auto x = dp[r] / dp[l];
cout << x[k].x << '\n';
}
}
int main()
{
cin.tie(nullptr);
ios::sync_with_stdio(false);
solve();
return 0;
}