結果
| 問題 | No.2369 Some Products |
| ユーザー |
 rniya
|
| 提出日時 | 2023-06-30 23:14:52 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 540 ms / 2,500 ms |
| コード長 | 42,284 bytes |
| コンパイル時間 | 4,277 ms |
| コンパイル使用メモリ | 248,808 KB |
| 実行使用メモリ | 208,820 KB |
| 最終ジャッジ日時 | 2023-09-21 17:32:08 |
| 合計ジャッジ時間 | 7,716 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / judge13 |
（要ログイン）
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 | 2 ms
4,380 KB |
| testcase_01 | AC | 2 ms
4,376 KB |
| testcase_02 | AC | 540 ms
208,660 KB |
| testcase_03 | AC | 519 ms
208,820 KB |
| testcase_04 | AC | 517 ms
208,728 KB |
| testcase_05 | AC | 39 ms
17,424 KB |
| testcase_06 | AC | 445 ms
208,720 KB |
| testcase_07 | AC | 37 ms
18,960 KB |
| testcase_08 | AC | 90 ms
42,384 KB |
| testcase_09 | AC | 31 ms
13,848 KB |
| testcase_10 | AC | 182 ms
76,908 KB |
| testcase_11 | AC | 338 ms
159,204 KB |
| testcase_12 | AC | 19 ms
10,048 KB |
| testcase_13 | AC | 218 ms
94,272 KB |
| testcase_14 | AC | 247 ms
110,828 KB |
ソースコード
#include <bits/stdc++.h>
#ifdef LOCAL
#include <debug.hpp>
#else
#define debug(...) void(0)
#endif
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
template <class mint,
int g = internal::primitive_root<mint::mod()>,
internal::is_static_modint_t<mint>* = nullptr>
struct fft_info {
static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);
std::array<mint, rank2 + 1> root; // root[i]^(2^i) == 1
std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1
std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;
std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;
fft_info() {
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 2; i++) {
rate2[i] = root[i + 2] * prod;
irate2[i] = iroot[i + 2] * iprod;
prod *= iroot[i + 2];
iprod *= root[i + 2];
}
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 3; i++) {
rate3[i] = root[i + 3] * prod;
irate3[i] = iroot[i + 3] * iprod;
prod *= iroot[i + 3];
iprod *= root[i + 3];
}
}
}
};
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::ceil_pow2(n);
static const fft_info<mint> info;
int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len < h) {
if (h - len == 1) {
int p = 1 << (h - len - 1);
mint rot = 1;
for (int s = 0; s < (1 << len); s++) {
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
if (s + 1 != (1 << len))
rot *= info.rate2[bsf(~(unsigned int)(s))];
}
len++;
} else {
// 4-base
int p = 1 << (h - len - 2);
mint rot = 1, imag = info.root[2];
for (int s = 0; s < (1 << len); s++) {
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto mod2 = 1ULL * mint::mod() * mint::mod();
auto a0 = 1ULL * a[i + offset].val();
auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
auto a1na3imag =
1ULL * mint(a1 + mod2 - a3).val() * imag.val();
auto na2 = mod2 - a2;
a[i + offset] = a0 + a2 + a1 + a3;
a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
if (s + 1 != (1 << len))
rot *= info.rate3[bsf(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::ceil_pow2(n);
static const fft_info<mint> info;
int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint irot = 1;
for (int s = 0; s < (1 << (len - 1)); s++) {
int offset = s << (h - len + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
irot.val();
;
}
if (s + 1 != (1 << (len - 1)))
irot *= info.irate2[bsf(~(unsigned int)(s))];
}
len--;
} else {
// 4-base
int p = 1 << (h - len);
mint irot = 1, iimag = info.iroot[2];
for (int s = 0; s < (1 << (len - 2)); s++) {
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
auto a0 = 1ULL * a[i + offset + 0 * p].val();
auto a1 = 1ULL * a[i + offset + 1 * p].val();
auto a2 = 1ULL * a[i + offset + 2 * p].val();
auto a3 = 1ULL * a[i + offset + 3 * p].val();
auto a2na3iimag =
1ULL *
mint((mint::mod() + a2 - a3) * iimag.val()).val();
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] =
(a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
a[i + offset + 2 * p] =
(a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
irot2.val();
a[i + offset + 3 * p] =
(a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
irot3.val();
}
if (s + 1 != (1 << (len - 2)))
irot *= info.irate3[bsf(~(unsigned int)(s))];
}
len -= 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint>& a,
const std::vector<mint>& b) {
int n = int(a.size()), m = int(b.size());
std::vector<mint> ans(n + m - 1);
if (n < m) {
for (int j = 0; j < m; j++) {
for (int i = 0; i < n; i++) {
ans[i + j] += a[i] * b[j];
}
}
} else {
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
}
return ans;
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(const std::vector<mint>& a,
const std::vector<mint>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++) {
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++) {
b2[i] = mint(b[i]);
}
auto c2 = convolution(move(a2), move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
c[i] = c2[i].val();
}
return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
const std::vector<long long>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
static constexpr unsigned long long MOD1 = 754974721; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static constexpr unsigned long long i1 =
internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr unsigned long long i2 =
internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr unsigned long long i3 =
internal::inv_gcd(MOD1 * MOD2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
unsigned long long x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
// B = 2^63, -B <= x, r(real value) < B
// (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
// r = c1[i] (mod MOD1)
// focus on MOD1
// r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
// r = x,
// x - M' + (0 or 2B),
// x - 2M' + (0, 2B or 4B),
// x - 3M' + (0, 2B, 4B or 6B) (without mod!)
// (r - x) = 0, (0)
// - M' + (0 or 2B), (1)
// -2M' + (0 or 2B or 4B), (2)
// -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
// we checked that
// ((1) mod MOD1) mod 5 = 2
// ((2) mod MOD1) mod 5 = 3
// ((3) mod MOD1) mod 5 = 4
long long diff =
c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
if (diff < 0) diff += MOD1;
static constexpr unsigned long long offset[5] = {
0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
} // namespace atcoder
template <typename T> struct FormalPowerSeries : std::vector<T> {
private:
using std::vector<T>::vector;
using FPS = FormalPowerSeries;
void shrink() {
while (this->size() and this->back() == T(0)) this->pop_back();
}
FPS pre(size_t sz) const { return FPS(this->begin(), this->begin() + std::min(this->size(), sz)); }
FPS rev() const {
FPS ret(*this);
std::reverse(ret.begin(), ret.end());
return ret;
}
FPS operator>>(size_t sz) const {
if (this->size() <= sz) return {};
return FPS(this->begin() + sz, this->end());
}
FPS operator<<(size_t sz) const {
if (this->empty()) return {};
FPS ret(*this);
ret.insert(ret.begin(), sz, T(0));
return ret;
}
public:
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];
shrink();
return *this;
}
FPS& operator+=(const T& v) {
if (this->empty()) this->resize(1);
(*this)[0] += v;
shrink();
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];
shrink();
return *this;
}
FPS& operator-=(const T& v) {
if (this->empty()) this->resize(1);
(*this)[0] -= v;
shrink();
return *this;
}
FPS& operator*=(const FPS& r) {
auto res = atcoder::convolution(*this, r);
return *this = {res.begin(), res.end()};
}
FPS& operator*=(const T& v) {
for (auto& x : (*this)) x *= v;
shrink();
return *this;
}
FPS& operator/=(const FPS& r) {
if (this->size() < r.size()) {
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
return *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 T& v) const { return FPS(*this) += v; }
FPS operator-(const FPS& r) const { return FPS(*this) -= r; }
FPS operator-(const T& v) const { return FPS(*this) -= v; }
FPS operator*(const FPS& r) const { return FPS(*this) *= r; }
FPS operator*(const T& 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;
for (auto& v : ret) v = -v;
return ret;
}
FPS differential() const {
const int n = (int)this->size();
FPS ret(std::max(0, n - 1));
for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
return ret;
}
FPS integral() const {
const int n = (int)this->size();
FPS ret(n + 1);
ret[0] = T(0);
if (n > 0) ret[1] = T(1);
auto mod = T::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;
}
FPS inv(int deg = -1) const {
assert((*this)[0] != T(0));
const int n = (int)this->size();
if (deg == -1) deg = n;
FPS ret{(*this)[0].inv()};
ret.reserve(deg);
for (int d = 1; d < deg; d <<= 1) {
FPS f(d << 1), g(d << 1);
std::copy(this->begin(), this->begin() + std::min(n, d << 1), f.begin());
std::copy(ret.begin(), ret.end(), g.begin());
atcoder::internal::butterfly(f);
atcoder::internal::butterfly(g);
for (int i = 0; i < (d << 1); i++) f[i] *= g[i];
atcoder::internal::butterfly_inv(f);
std::fill(f.begin(), f.begin() + d, T(0));
atcoder::internal::butterfly(f);
for (int i = 0; i < (d << 1); i++) f[i] *= g[i];
atcoder::internal::butterfly_inv(f);
T iz = T(d << 1).inv();
iz *= -iz;
for (int i = d; i < std::min(d << 1, deg); i++) ret.push_back(f[i] * iz);
}
return ret.pre(deg);
}
FPS log(int deg = -1) const {
assert((*this)[0] == T(1));
if (deg == -1) deg = (int)this->size();
return (differential() * inv(deg)).pre(deg - 1).integral();
}
FPS sqrt(const std::function<T(T)>& get_sqrt, int deg = -1) const {
const int n = this->size();
if (deg == -1) deg = n;
if (this->empty()) return FPS(deg, 0);
if ((*this)[0] == T(0)) {
for (int i = 1; i < n; i++) {
if ((*this)[i] != T(0)) {
if (i & 1) return {};
if (deg - i / 2 <= 0) break;
auto ret = (*this >> i).sqrt(get_sqrt, deg - i / 2);
if (ret.empty()) return {};
ret = ret << (i / 2);
if ((int)ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return FPS(deg, T(0));
}
auto sqrtf0 = T(get_sqrt((*this)[0]));
if (sqrtf0 * sqrtf0 != (*this)[0]) return {};
FPS ret{sqrtf0};
T inv2 = T(2).inv();
for (int i = 1; i < deg; i <<= 1) ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
return ret.pre(deg);
}
/**
* @brief Exp of Formal Power Series
*
* @see https://arxiv.org/pdf/1301.5804.pdf
*/
FPS exp(int deg = -1) const {
assert(this->empty() or (*this)[0] == T(0));
if (this->size() <= 1) return {T(1)};
if (deg == -1) deg = (int)this->size();
FPS inv;
inv.reserve(deg + 1);
inv.push_back(T(0));
inv.push_back(T(1));
auto inplace_integral = [&](FPS& F) -> void {
const int n = (int)F.size();
auto mod = T::mod();
while ((int)inv.size() <= n) {
int i = inv.size();
inv.push_back(-inv[mod % i] * (mod / i));
}
F.insert(F.begin(), T(0));
for (int i = 1; i <= n; i++) F[i] *= inv[i];
};
auto inplace_differential = [](FPS& F) -> void {
if (F.empty()) return;
F.erase(F.begin());
for (size_t i = 0; i < F.size(); i++) F[i] *= T(i + 1);
};
FPS f{1, (*this)[1]}, g{T(1)}, g_fft{T(1), T(1)};
for (int m = 2; m < deg; m <<= 1) {
const T iz1 = T(m).inv(), iz2 = T(m << 1).inv();
auto f_fft = f;
f_fft.resize(m << 1);
atcoder::internal::butterfly(f_fft);
{
// Step 2.a'
FPS _g(m);
for (int i = 0; i < m; i++) _g[i] = f_fft[i] * g_fft[i];
atcoder::internal::butterfly_inv(_g);
std::fill(_g.begin(), _g.begin() + (m >> 1), T(0));
atcoder::internal::butterfly(_g);
for (int i = 0; i < m; i++) _g[i] *= -g_fft[i] * iz1 * iz1;
atcoder::internal::butterfly_inv(_g);
g.insert(g.end(), _g.begin() + (m >> 1), _g.end());
g_fft = g;
g_fft.resize(m << 1);
atcoder::internal::butterfly(g_fft);
}
FPS x(this->begin(), this->begin() + std::min((int)this->size(), m));
{
// Step 2.b'
x.resize(m);
inplace_differential(x);
x.push_back(T(0));
atcoder::internal::butterfly(x);
}
{
// Step 2.c'
for (int i = 0; i < m; i++) x[i] *= f_fft[i] * iz1;
atcoder::internal::butterfly_inv(x);
}
{
// Step 2.d' and 2.e'
x -= f.differential();
x.resize(m << 1);
for (int i = 0; i < m - 1; i++) x[m + i] = x[i], x[i] = T(0);
atcoder::internal::butterfly(x);
for (int i = 0; i < (m << 1); i++) x[i] *= g_fft[i] * iz2;
atcoder::internal::butterfly_inv(x);
}
{
// Step 2.f'
x.pop_back();
inplace_integral(x);
for (int i = m; i < std::min((int)this->size(), m << 1); i++) x[i] += (*this)[i];
std::fill(x.begin(), x.begin() + m, T(0));
}
{
// Step 2.g' and 2.h'
atcoder::internal::butterfly(x);
for (int i = 0; i < (m << 1); i++) x[i] *= f_fft[i] * iz2;
atcoder::internal::butterfly_inv(x);
f.insert(f.end(), x.begin() + m, x.end());
}
}
return FPS{f.begin(), f.begin() + deg};
}
FPS pow(int64_t k, int deg = -1) const {
const int n = (int)this->size();
if (deg == -1) deg = n;
if (k == 0) {
auto res = FPS(deg, T(0));
res[0] = T(1);
return res;
}
for (int i = 0; i < n; i++) {
if ((*this)[i] != T(0)) {
if (i >= (deg + k - 1) / k) return FPS(deg, T(0));
T rev = (*this)[i].inv();
FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg) * ((*this)[i].pow(k));
ret = (ret << (i * k)).pre(deg);
if ((int)ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return FPS(deg, T(0));
}
T eval(T x) const {
T ret = 0, w = 1;
for (const auto& v : *this) ret += w * v, w *= x;
return ret;
}
static FPS product_of_polynomial_sequence(const std::vector<FPS>& fs) {
if (fs.empty()) return {T(1)};
auto comp = [](const FPS& f, const FPS& g) { return f.size() > g.size(); };
std::priority_queue<FPS, std::vector<FPS>, decltype(comp)> pq{comp};
for (const auto& f : fs) pq.emplace(f);
while (pq.size() > 1) {
auto f = pq.top();
pq.pop();
auto g = pq.top();
pq.pop();
pq.emplace(f * g);
}
return pq.top();
}
static FPS pow_sparse(const std::vector<std::pair<int, T>>& f, int64_t k, int n) {
assert(k >= 0);
int d = f.size(), offset = 0;
while (offset < d and f[offset].second == 0) offset++;
FPS res(n, 0);
if (offset == d) {
if (k == 0) res[0]++;
return res;
}
if (f[offset].first > 0) {
int deg = f[offset].first;
if (k > (n - 1) / deg) return res;
std::vector<std::pair<int, T>> g(f.begin() + offset, f.end());
for (auto& p : g) p.first -= deg;
auto tmp = pow_sparse(g, k, n - k * deg);
for (int i = 0; i < n - k * deg; i++) res[k * deg + i] = tmp[i];
return res;
}
std::vector<T> invs(n + 1);
invs[0] = T(0);
invs[1] = T(1);
auto mod = T::mod();
for (int i = 2; i <= n; i++) invs[i] = -invs[mod % i] * (mod / i);
res[0] = f[0].second.pow(k);
T coef = f[0].second.inv();
for (int i = 1; i < n; i++) {
for (int j = 1; j < d; j++) {
if (i - f[j].first < 0) break;
res[i] += f[j].second * res[i - f[j].first] * (T(k) * f[j].first - (i - f[j].first));
}
res[i] *= invs[i] * coef;
}
return res;
}
FPS taylor_shift(T c) const {
FPS f(*this);
const int n = f.size();
std::vector<T> fac(n), finv(n);
fac[0] = 1;
for (int i = 1; i < n; i++) {
fac[i] = fac[i - 1] * i;
f[i] *= fac[i];
}
finv[n - 1] = fac[n - 1].inv();
for (int i = n - 1; i > 0; i--) finv[i - 1] = finv[i] * i;
std::reverse(f.begin(), f.end());
FPS g(n);
g[0] = T(1);
for (int i = 1; i < n; i++) g[i] = g[i - 1] * c * finv[i] * fac[i - 1];
f = (f * g).pre(n);
std::reverse(f.begin(), f.end());
for (int i = 0; i < n; i++) f[i] *= finv[i];
return f;
}
};
using namespace std;
typedef long long ll;
#define all(x) begin(x), end(x)
constexpr int INF = (1 << 30) - 1;
constexpr long long IINF = (1LL << 60) - 1;
constexpr int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
template <class T> istream& operator>>(istream& is, vector<T>& v) {
for (auto& x : v) is >> x;
return is;
}
template <class T> ostream& operator<<(ostream& os, const vector<T>& v) {
auto sep = "";
for (const auto& x : v) os << exchange(sep, " ") << x;
return os;
}
template <class T, class U = T> bool chmin(T& x, U&& y) { return y < x and (x = forward<U>(y), true); }
template <class T, class U = T> bool chmax(T& x, U&& y) { return x < y and (x = forward<U>(y), true); }
template <class T> void mkuni(vector<T>& v) {
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
}
template <class T> int lwb(const vector<T>& v, const T& x) { return lower_bound(begin(v), end(v), x) - begin(v); }
using mint = atcoder::modint998244353;
using FPS = FormalPowerSeries<mint>;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int N;
cin >> N;
vector<int> P(N);
vector<FPS> dp;
dp.emplace_back(FPS{1});
for (int i = 0; i < N; i++) {
int p;
cin >> p;
auto v = dp.back();
v.emplace_back(0);
for (int j = int(v.size()) - 2; j >= 0; j--) v[j + 1] += v[j] * p;
dp.emplace_back(v);
P[i] = p;
}
vector<FPS> invs(N + 1);
invs.back() = dp.back().inv();
for (int i = N - 1; i >= 0; i--) {
auto v = invs[i + 1];
v.emplace_back(0);
for (int j = int(v.size()) - 2; j >= 0; j--) v[j + 1] += v[j] * P[i];
invs[i] = v;
}
auto query = [&](int A, int B, int K) -> mint {
mint res = 0;
for (int i = 0; i < int(invs[A].size()); i++) {
int j = K - i;
if (0 <= j and j < int(dp[B].size())) res += invs[A][i] * dp[B][j];
}
return res;
};
int Q;
cin >> Q;
for (; Q--;) {
int A, B, K;
cin >> A >> B >> K;
cout << query(--A, B, K).val() << '\n';
}
return 0;
}