結果
| 問題 |
No.2062 Sum of Subset mod 999630629
|
| コンテスト | |
| ユーザー |
 tomo0608
|
| 提出日時 | 2023-08-22 22:43:02 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 49,530 bytes |
| コンパイル時間 | 4,872 ms |
| コンパイル使用メモリ | 265,804 KB |
| 最終ジャッジ日時 | 2025-02-16 12:21:32 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 10 WA * 19 |
ソースコード
#pragma region competitive_programming
#ifdef __LOCAL
#define _GLIBCXX_DEBUG
#endif
#pragma GCC optimize("Ofast")
#include<bits/stdc++.h>
//#include<atcoder/dsu>
//#include "Rollback_dsu.hpp"
//#include "Partial_Persistent_DSU.hpp"
//#include "Number_Theory.hpp"
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
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;
}
};
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;
}
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);
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};
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
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
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);
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;
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
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
namespace tomo0608 {
std::istream& operator>>(std::istream& is, atcoder::modint998244353& a) { long long v; is >> v; a = v; return is; }
std::ostream& operator<<(std::ostream& os, const atcoder::modint998244353& a) { return os << a.val(); }
std::istream& operator>>(std::istream& is, atcoder::modint1000000007& a) { long long v; is >> v; a = v; return is; }
std::ostream& operator<<(std::ostream& os, const atcoder::modint1000000007& a) { return os << a.val(); }
template<int m> std::istream& operator>>(std::istream& is, atcoder::static_modint<m>& a) { long long v; is >> v; a = v; return is; }
template<int m> std::ostream& operator<<(std::ostream& os, const atcoder::static_modint<m>& a) { return os << a.val(); }
template<int m> std::istream& operator>>(std::istream& is, atcoder::dynamic_modint<m>& a) { long long v; is >> v; a = v; return is; }
template<int m> std::ostream& operator<<(std::ostream& os, const atcoder::dynamic_modint<m>& a) { return os << a.val(); }
// Binomial Coefficient of modint
template<class mint> struct BiCoef {
std::vector<mint> fact_, inv_, finv_;
constexpr BiCoef() {}
constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
init(n);
}
constexpr void init(int n) noexcept {
fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
int MOD = fact_[0].mod();
for (int i = 2; i < n; i++) {
fact_[i] = fact_[i - 1] * i;
inv_[i] = -inv_[MOD % i] * (MOD / i);
finv_[i] = finv_[i - 1] * inv_[i];
}
}
constexpr mint com(int n, int k) const noexcept {
if (n < k || n < 0 || k < 0)return 0;
return fact_[n] * finv_[k] * finv_[n - k];
}
constexpr mint perm(int n, int k) const noexcept {
if (n < k || n < 0 || k < 0)return 0;
return fact_[n] * finv_[n - k];
}
constexpr mint homo(int n, int r) { // The number of cases where k indistinguishable balls are put into n distinct boxes
if (n < 0 || r < 0)return 0;
return r == 0 ? 1 : com(n + r - 1, r);
}
constexpr mint second_stirling_number(int n, int r) { // The number of cases where n distinct balls are put into k indistinguishable boxes, with at least one ball in each box
mint ret = 0;
for (int i = 0; i <= r; i++) {
mint tmp = com(r, i) * mint(i).pow(n);
ret += ((r - i) & 1) ? -tmp : tmp;
}
return ret * finv_[r];
}
constexpr mint bell_number(int n, int r) { // The number of cases where n distinct balls are put into k indistinguishable boxes
if (n == 0) return 1;
r = std::min(r, n);
std::vector<mint> pref(r + 1);
pref[0] = 1;
for (int i = 1; i <= r; i++) {
if (i & 1) {
pref[i] = pref[i - 1] - finv_[i];
}
else {
pref[i] = pref[i - 1] + finv_[i];
}
}
mint ret = 0;
for (int i = 1; i <= r; i++) ret += mint(i).pow(n) * fact_[i] * pref[r - i];
return ret;
}
constexpr mint fact(int n) const noexcept {
if (n < 0)return 0;
return fact_[n];
}
constexpr mint inv(int n) const noexcept {
if (n < 0)return 0;
return inv_[n];
}
constexpr mint finv(int n) const noexcept {
if (n < 0)return 0;
return finv_[n];
}
inline mint operator()(int n, int k) { return com(n, k); }
constexpr mint com_naive(long long n, long long k) {
if (n < k || n < 0 || k < 0)return 0;
mint res = 1;
k = std::min(k, n - k);
for (int i = 1; i <= k; i++)res *= inv(i) * (n--);
return res;
}
};
} // namespace tomo0608
//typedef atcoder::modint1000000007 mint;
typedef atcoder::modint998244353 mint;
//#include "Matrix.hpp"
//#include<atcoder/convolution>
#include <algorithm>
#include <array>
#include <cassert>
#include <type_traits>
#include <vector>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
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 {
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 {
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;
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
namespace tomo0608 {
template<typename mint>
struct Formal_Power_Series : public std::vector<mint> {
using FPS = Formal_Power_Series;
using std::vector<mint>::vector;
using std::vector<mint>::operator=;
void shrink() {
while (this->size() && this->back() == mint(0))this->pop_back();
}
FPS& operator+=(const FPS& rhs) {
if (rhs.size() > this->size())this->resize(rhs.size());
for (int i = 0; i < (int)rhs.size();i++)(*this)[i] += rhs[i];
return *this;
}
FPS& operator-=(const FPS& rhs) {
if (rhs.size() > this->size())this->resize(rhs.size());
for (int i = 0; i < (int)rhs.size();i++)(*this)[i] -= rhs[i];
return *this;
}
FPS& operator+=(const mint& rhs) {
if (this->empty())this->resize(1);
(*this)[0] += rhs;
return *this;
}
FPS& operator-=(const mint& rhs) {
if (this->empty())this->resize(1);
(*this)[0] -= rhs;
return *this;
}
FPS& operator*=(const mint& rhs) {
for (auto& e : *this)e *= rhs;
return *this;
}
FPS& operator*=(const FPS& rhs) {
*this = atcoder::convolution((*this), rhs);
return *this;
}
FPS& operator/=(const mint& c) {
assert(c != mint(0));
*this *= c.inv();
return *this;
}
FPS& operator/=(const FPS& rhs) {
*this *= rhs.inv();
this->resize(rhs.size());
return *this;
}
friend FPS operator+(const FPS& lhs, const FPS& rhs) {
return FPS(lhs) += rhs;
}
friend FPS operator+(const FPS& lhs, const mint& rhs) {
return FPS(lhs) += rhs;
}
friend FPS operator-(const FPS& lhs, const FPS& rhs) {
return FPS(lhs) -= rhs;
}
friend FPS operator-(const FPS& lhs, const mint& rhs) {
return FPS(lhs) -= rhs;
}
friend FPS operator*(const FPS& lhs, const FPS& rhs) {
return FPS(lhs) *= rhs;
}
friend FPS operator*(const FPS& lhs, const mint& rhs) {
return FPS(lhs) *= rhs;
}
friend FPS operator/(const FPS& lhs, const mint& rhs) {
return FPS(lhs) /= rhs;
}
// friend std::ostream& operator<<(std::ostream& os, FPS& f) {
// for (int i = 0; i < f.size(); i++) {
// os << f[i] << (i + 1 == f.size() ? "\n" : " ");
// }
// return (os);
// }
FPS inv(int deg = -1) const {
assert(this->front() != mint(0));
if (deg == -1)deg = this->size();
FPS res = { this->front().inv() };
for (int d = 1; d < deg; d <<= 1) {
FPS f(2 * d), g(2 * d);
for (int j = 0; j < std::min((int)this->size(), 2 * d); j++)f[j] = (*this)[j];
for (int j = 0; j < d; j++)g[j] = res[j];
atcoder::internal::butterfly(f);
atcoder::internal::butterfly(g);
for (int j = 0; j < 2 * d; j++)f[j] *= g[j];
atcoder::internal::butterfly_inv(f);
f /= 2 * d;
for (int j = 0; j < d; j++) {
f[j] = f[j + d];
f[j + d] = 0;
}
atcoder::internal::butterfly(f);
for (int j = 0; j < 2 * d; j++)f[j] *= -g[j];
atcoder::internal::butterfly_inv(f);
f /= 2 * d;
for (int j = 0; j < d; j++)res.emplace_back(f[j]);
}
res.resize(deg);
return res;
}
FPS operator-() const {
FPS res(*this);
for (auto& e : res) e = -e;
return res;
}
FPS derivative() const {
FPS res(this->begin() + 1, this->end());
res.emplace_back(0);
for (int j = 0; j < res.size(); j++)res[j] *= (j + 1);
return res;
}
FPS integral(bool truncate = true) const {
FPS res(this->size() + 1 - truncate, 0);
for (int j = 0; j < this->size() - truncate; j++)res[j + 1] = (*this)[j] / (j + 1);
return res;
}
FPS log() const {
FPS f = this->derivative();
f /= (*this);
return f.integral();
}
// https://arxiv.org/pdf/1301.5804.pdf
FPS exp(int deg = -1) const {
assert(this->front() == mint(0));
if (deg == -1)deg = this->size();
FPS f = { 1 }, g = { 1 };
for (int d = 1; d < deg; d <<= 1) {
FPS f_next(f);
f_next.resize(2 * d, 0);
atcoder::internal::butterfly(f_next);
g.resize(2 * d, 0);
atcoder::internal::butterfly(g);
for (int j = 0; j < 2 * d; j++)g[j] = 2 * g[j] - f_next[j] * g[j] * g[j];
atcoder::internal::butterfly_inv(g);
g /= 2 * d;
g.resize(d);
FPS q(2 * d);
for (int j = 0; j < d && j < this->size() - 1; j++)q[j] = (*this)[j + 1] * (j + 1);
FPS w(2 * d);
FPS G(g);
G.resize(2 * d, 0);
atcoder::internal::butterfly(G);
for (int j = 0; j < 2 * d; j++)w[j] = f_next[j] * G[j];
atcoder::internal::butterfly_inv(w);
w /= 2 * d;
for (int j = 0; j < d; j++) {
w[j] = w[j + d];
w[j + d] = 0;
}
atcoder::internal::butterfly(w);
atcoder::internal::butterfly(q);
for (int j = 0; j < 2 * d; j++)w[j] *= q[j];
atcoder::internal::butterfly_inv(w);
w /= 2 * d;
FPS df(f.derivative());
df.resize(2 * d, 0);
atcoder::internal::butterfly(df);
for (int j = 0;j < 2 * d;j++)df[j] *= G[j];
atcoder::internal::butterfly_inv(df);
df /= 2 * d;
for (int j = 0; j < d;j++) {
w[j + d] = w[j];
w[j] = 0;
}
w -= df;
w = w.integral();
for (int j = 0; j < 2 * d && j < this->size(); j++)w[j] += (*this)[j];
for (int j = 0; j < d;j++) {
w[j] = w[j + d];
w[j + d] = 0;
}
atcoder::internal::butterfly(w);
for (int j = 0; j < 2 * d; j++)f_next[j] *= w[j];
atcoder::internal::butterfly_inv(f_next);
f_next /= 2 * d;
f.resize(2 * d, 0);
for (int j = 0; j < d; j++)f[j + d] = f_next[j];
}
f.resize(deg);
return f;
}
FPS pow(long long m) const {
int n = this->size();
if (m == 0) {
auto res = FPS(n, 0);
res[0] = 1;
return res;
}
int l = std::find_if(this->begin(), this->end(), [](mint x) {return x != mint(0);}) - this->begin();
if (l == this->size() || (l && m >= (n + l - 1) / l))return FPS(n, 0);
FPS res(this->begin() + l, this->end());
mint c = (*this)[l];
res /= c;
res.resize(n, 0);
res = (res.log() * mint(m)).exp();
res.erase(res.begin() + (n - m * l), res.end());
res *= c.pow(m);
std::reverse(res.begin(), res.end());
res.resize(n, 0);
std::reverse(res.begin(), res.end());
return res;
}
};
// for sparse fps
template <typename mint>
Formal_Power_Series<mint> positive_unit_fractions(int n) { // res[i] = 1 / i, res[0] = 0 length: n+1
static const int mod = mint::mod();
static Formal_Power_Series<mint> res = { 0, 1 };
assert(0 < n);
if (n >= mod) n -= mod;
while (int(res.size()) <= n) {
int num = res.size();
int q = (mod + num - 1) / num;
res.emplace_back(res[num * q - mod] * mint(q));
}
return res;
}
template<typename mint>
std::vector<std::pair<int, mint>> compress_fps(const Formal_Power_Series<mint>& f) {
int n = f.size();
std::vector<std::pair<int, mint>> cf;
for (int i = 0; i < n; i++) {
if (f[i] != 0)cf.emplace_back(i, f[i]);
}
return cf;
}
template<typename mint>
Formal_Power_Series<mint> mul_sparse(const Formal_Power_Series<mint>& f, const Formal_Power_Series<mint>& g) {
int n = f.size(), m = g.size();
auto cf = compress_fps<mint>(f), cg = compress_fps<mint>(g);
Formal_Power_Series<mint> h(n + m - 1);
for (auto [i, p] : cf)for (auto [j, q] : cg)h[i + j] += p * q;
return h;
}
template<typename mint>
Formal_Power_Series<mint> inv_sparse(const Formal_Power_Series<mint>& f, int deg = -1) {
assert(f[0] != 0);
if (deg == -1)deg = f.size();
auto cf = compress_fps<mint>(f);
Formal_Power_Series<mint> f_inv(deg);
f_inv[0] = f[0].inv();
for (int i = 1; i < deg; i++) {
for (auto [k, p] : cf) {
if (i - k < 0)break;
f_inv[i] -= f_inv[i - k] * p;
}
f_inv[i] *= f_inv[0];
}
return f_inv;
}
template<typename mint>
Formal_Power_Series<mint> exp_sparse(const Formal_Power_Series<mint>& f, int deg = -1) {
assert(f[0] == 0);
if (deg == -1)deg = f.size();
auto cf = compress_fps<mint>(f);
Formal_Power_Series<mint> f_exp(deg);
Formal_Power_Series<mint> inv_num = positive_unit_fractions<mint>(deg);
f_exp[0] = 1;
for (int i = 1; i < deg; i++) {
for (auto [k, p] : cf) {
if (i - k < 0)break;
f_exp[i] += f_exp[i - k] * p * k;
}
f_exp[i] *= inv_num[i];
}
return f_exp;
}
template<typename mint>
Formal_Power_Series<mint> log_sparse(const Formal_Power_Series<mint>& f, int deg = -1) {
assert(f[0] == 1);
if (deg == -1)deg = f.size();
Formal_Power_Series<mint> df = f.derivative();
Formal_Power_Series<mint> df_log = mul_sparse<mint>(df, inv_sparse<mint>(f));
Formal_Power_Series<mint> f_log = df_log.integral();
f_log.resize(deg);
return f_log;
}
template<typename mint>
Formal_Power_Series<mint> __pow_sparse_const_1(const Formal_Power_Series<mint>& f, long long k, int deg) {
int n = f.size();
assert(n > 0 && f[0] == 1);
auto cf = compress_fps<mint>(f);
Formal_Power_Series<mint> f_pow_k(deg);
Formal_Power_Series<mint> inv_num = positive_unit_fractions<mint>(deg);
f_pow_k[0] = 1;
for (int i = 1; i < deg; i++) {
for (const auto& [j, coef] : cf) {
if (i - j < 0) break;
f_pow_k[i] += (mint(k) * mint(j) - mint(i - j)) * coef * f_pow_k[i - j];
}
f_pow_k[i] *= inv_num[i];
}
return f_pow_k;
}
template<typename mint>
Formal_Power_Series<mint> pow_sparse(const Formal_Power_Series<mint>& f, long long k, int deg = -1) {
int n = f.size();
if (deg < 0)deg = n;
assert(k >= 0);
if (k == 0) {
Formal_Power_Series<mint> res(deg, 0);
if (deg)res[0] = 1;
return res;
}
int l = std::find_if(f.begin(), f.end(), [](mint x) {return x != mint(0);}) - f.begin();
if (l == f.size() || (l && k >= (deg + l - 1) / l))return Formal_Power_Series<mint>(deg, 0);
Formal_Power_Series<mint> res(f.begin() + l, f.end());
mint c = f[l];
res /= c;
res.resize(deg, 0);
res = __pow_sparse_const_1<mint>(res, k, deg);
res.erase(res.begin() + (deg - k * l), res.end());
res *= c.pow(k);
std::reverse(res.begin(), res.end());
res.resize(deg, 0);
std::reverse(res.begin(), res.end());
return res;
}
} // namespace tomo0608
//#include "Bit_Convolution.hpp"
//#include<atcoder/maxflow>
//#include<atcoder/mincostflow>
//#include "Primal_Dual.hpp"
//#include "maxflow_mincap.hpp"
//#include<atcoder/fenwicktree>
//#include<atcoder/segtree>
//#include<atcoder/lazysegtree>
//#include "2D_Segment_Tree.hpp"
//#include "DisjointSparseTable.hpp"
//#include "SWAG.hpp"
//#include "Mo_algorithm.hpp"
//#include "Heavy_Light_Decomposition.hpp"
//#include "Binary_Trie.hpp"
//#include "LCT.hpp"
//#include "Slope_Trick.hpp"
//#include<atcoder/string>
//#include<atcoder/scc>
//#include "TwoEdgeCC.hpp"
namespace tomo0608 {
typedef long long ll;
typedef long double ld;
template <class T> using V = std::vector<T>;
template <class T> using VV = V<V<T>>;
template <class T> using VVV = V<VV<T>>;
typedef std::pair<int, int> pii;
typedef std::pair<long long, long long> pll;
template<class... T>void input(T&... a) { (std::cin >> ... >> a); };
#define INT(...) int __VA_ARGS__; IN(__VA_ARGS__)
#define LL(...) long long __VA_ARGS__; IN(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; IN(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; IN(__VA_ARGS__)
#define VEC(type, name, size) std::vector<type> name(size);IN(name)
#define VECVEC(type, name, h, w) std::vector<std::vector<type>> name(h, std::vector<type>(w));IN(name)
template<class T1, class T2> std::istream& operator>>(std::istream& is, std::pair<T1, T2>& p) { is >> p.first >> p.second; return is; }
template<class T1, class T2> std::ostream& operator<<(std::ostream& os, const std::pair<T1, T2>& p) { os << '(' << p.first << ", " << p.second << ')'; return os; }
template<class T> std::istream& operator>>(std::istream& is, std::vector<T>& v) { for (auto& e : v) is >> e; return is; }
template<class T> std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) { for (auto& e : v) os << e << ' '; return os; }
template<typename T> std::ostream& operator << (std::ostream& os, std::set<T>& set_var) { os << "{"; for (auto itr = set_var.begin(); itr != set_var.end(); itr++) { os << *itr;++itr;if (itr != set_var.end()) os << ", ";itr--; }os << "}";return os; }
template <typename T, typename U> std::ostream& operator<<(std::ostream& os, std::map<T, U>& map_var) { os << "{";for (auto itr = map_var.begin(); itr != map_var.end(); itr++) { os << *itr;itr++;if (itr != map_var.end()) os << ", ";itr--; }os << "}";return os; }
void IN() {}
template <class Head, class... Tail> void IN(Head& head, Tail &...tail) {
std::cin >> head;
IN(tail...);
}
void print() { std::cout << '\n'; }
template<class T, class... Ts>void print(const T& a, const Ts&... b) { std::cout << a; (std::cout << ... << (std::cout << ' ', b)); std::cout << '\n'; }
void drop() { std::cout << '\n';exit(0); }
template<class T, class... Ts>void drop(const T& a, const Ts&... b) { std::cout << a; (std::cout << ... << (std::cout << ' ', b)); std::cout << '\n';exit(0); }
#ifdef __LOCAL
void debug_out() { std::cerr << std::endl; }
template < class Head, class... Tail> void debug_out(Head H, Tail... T) { std::cerr << ' ' << H; debug_out(T...); }
#define debug(...) std::cerr << 'L' << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) std::cerr << 'L' << __LINE__ << " " << #x << " = " << (x) << std::endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
#define rep1(a) for(long long i = 0; i < a; i++)
#define rep2(i, a) for(long long i = 0; i < a; i++)
#define rep3(i, a, b) for(long long i = a; i < b; i++)
#define rep4(i, a, b, c) for(long long i = a; i < b; i += c)
#define drep1(a) for(long long i = a-1; i >= 0; i--)
#define drep2(i, a) for(long long i = a-1; i >= 0; i--)
#define drep3(i, a, b) for(long long i = a-1; i >= b; i--)
#define drep4(i, a, b, c) for(long long i = a-1; i >= b; i -= c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define drep(...) overload4(__VA_ARGS__, drep4, drep3, drep2, drep1)(__VA_ARGS__)
#define endl '\n'
} // namespace tomo0608
namespace tomo0608 {
#define ALL(x) x.begin(),x.end()
template <class T = long long, class S> T SUM(const S& v) { return accumulate(ALL(v), T(0)); }
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define SORT(v) sort(ALL(v))
#define REVERSE(v) reverse(ALL(v))
#define RSORT(v) sort(ALL(v)); reverse(ALL(v))
#define UNIQUE(x) SORT(x), x.erase(unique(ALL(x)), x.end())
#define lb(c, x) distance((c).begin(), lower_bound(ALL(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(ALL(c), (x)))
template <typename T> void zip(std::vector<T>& x) { std::vector<T> y = x;UNIQUE(y);for (int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); } }
template<class T> using priority_queue_rev = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template<class T, class U> inline bool chmax(T& a, const U& b) { if (a < b) { a = b; return 1; } return 0; }
template<class T, class U> inline bool chmin(T& a, const U& b) { if (a > b) { a = b; return 1; } return 0; }
template<class T> inline int count_between(std::vector<T>& a, T l, T r) { return lower_bound(ALL(a), r) - lower_bound(ALL(a), l); } // [l, r)
#define bittest(n, k) (((n) >> (k)) & 1)
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int lowbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
#define perm(v) for(bool permrepflag = true; (permrepflag ? exchange(permrepflag, false) : next_permutation(ALL(v)));)
template <typename T, typename S> T ceil(T x, S y) {
assert(y);
return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y));
}
template <typename T, typename S> T floor(T x, S y) {
assert(y);
return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1)));
}
}
using namespace atcoder;
using namespace std;
using namespace tomo0608;
int dx[8] = { 1, 0, -1, 0, 1, 1, -1, -1 };
int dy[8] = { 0, 1, 0, -1, 1, -1, -1, 1 };
// インタラクティブ問題のときは出力するたびにcout.flush();を忘れない!!!!!
void solve();
int main() {
std::cin.tie(0);
std::ios_base::sync_with_stdio(false);
std::cout << std::setprecision(20);
int codeforces = 1;
//cin >> codeforces;
while (codeforces--) {
solve();
}
return 0;
}
#pragma endregion
const int m2 = 999630629;
typedef Formal_Power_Series<mint> fps;
void solve() {
INT(n);
VEC(ll, a, n);
ll sum_a = SUM(a); // sum_a < 2 * m2
mint ans = sum_a * mint(2).pow(n-1);
if(sum_a < m2)drop(ans);
// \sum_{i \in S}a_i >= m2となるようなSの個数を求める
// \sum_{i \in T}a_i <= sum_a - m2となるようなTの個数を求めればよい
ll sz = sum_a - m2 + 1;
fps sum_log(sz);
BiCoef<mint> bc(sz);
rep(i, n){
// log(1 + x^a_i)を求める
for(int j = a[i], num = 1, c = 1; j < sz; j += a[i], num++, c *= -1){
sum_log[j] += bc.inv(num) * c;
}
}
fps prd = sum_log.exp();
mint cnt = mint(2).pow(n);
rep(i, sz)cnt -= prd[i];
print(ans - cnt * m2);
}