結果
| 問題 |
No.2062 Sum of Subset mod 999630629
|
| コンテスト | |
| ユーザー |
 torisasami4
|
| 提出日時 | 2022-08-26 22:13:02 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,274 ms / 5,000 ms |
| コード長 | 21,729 bytes |
| コンパイル時間 | 4,253 ms |
| コンパイル使用メモリ | 269,308 KB |
| 最終ジャッジ日時 | 2025-01-31 05:00:29 |
|
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 * 29 |
ソースコード
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define per(i, n) for (int i = (n)-1; 0 <= i; i--)
#define rep2(i, l, r) for (int i = (l); i < int(r); i++)
#define per2(i, l, r) for (int i = (r)-1; int(l) <= i; i--)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
template <typename T>
void print(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++)
cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
if (v.empty())
cout << '\n';
}
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <typename T>
bool chmax(T &x, const T &y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
bool chmin(T &x, const T &y) {
return (x > y) ? (x = y, true) : false;
}
template <class T>
using minheap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <class T>
using maxheap = std::priority_queue<T>;
template <typename T>
int lb(const vector<T> &v, T x) {
return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, T x) {
return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
void rearrange(vector<T> &v) {
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
}
// __int128_t gcd(__int128_t a, __int128_t b) {
// if (a == 0)
// return b;
// if (b == 0)
// return a;
// __int128_t cnt = a % b;
// while (cnt != 0) {
// a = b;
// b = cnt;
// cnt = a % b;
// }
// return b;
// }
long long extGCD(long long a, long long b, long long &x, long long &y) {
if (b == 0) {
x = 1;
y = 0;
return a;
}
long long d = extGCD(b, a % b, y, x);
y -= a / b * x;
return d;
}
struct UnionFind {
vector<int> data;
int num;
UnionFind(int sz) {
data.assign(sz, -1);
num = sz;
}
bool unite(int x, int y) {
x = find(x), y = find(y);
if (x == y)
return (false);
if (data[x] > data[y])
swap(x, y);
data[x] += data[y];
data[y] = x;
num--;
return (true);
}
int find(int k) {
if (data[k] < 0)
return (k);
return (data[k] = find(data[k]));
}
int size(int k) {
return (-data[find(k)]);
}
bool same(int x, int y) {
return find(x) == find(y);
}
int operator[](int k) {
return find(k);
}
};
template <int mod>
struct Mod_Int {
int x;
Mod_Int() : x(0) {
}
Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {
}
static int get_mod() {
return mod;
}
Mod_Int &operator+=(const Mod_Int &p) {
if ((x += p.x) >= mod)
x -= mod;
return *this;
}
Mod_Int &operator-=(const Mod_Int &p) {
if ((x += mod - p.x) >= mod)
x -= mod;
return *this;
}
Mod_Int &operator*=(const Mod_Int &p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
Mod_Int &operator/=(const Mod_Int &p) {
*this *= p.inverse();
return *this;
}
Mod_Int &operator++() {
return *this += Mod_Int(1);
}
Mod_Int operator++(int) {
Mod_Int tmp = *this;
++*this;
return tmp;
}
Mod_Int &operator--() {
return *this -= Mod_Int(1);
}
Mod_Int operator--(int) {
Mod_Int tmp = *this;
--*this;
return tmp;
}
Mod_Int operator-() const {
return Mod_Int(-x);
}
Mod_Int operator+(const Mod_Int &p) const {
return Mod_Int(*this) += p;
}
Mod_Int operator-(const Mod_Int &p) const {
return Mod_Int(*this) -= p;
}
Mod_Int operator*(const Mod_Int &p) const {
return Mod_Int(*this) *= p;
}
Mod_Int operator/(const Mod_Int &p) const {
return Mod_Int(*this) /= p;
}
bool operator==(const Mod_Int &p) const {
return x == p.x;
}
bool operator!=(const Mod_Int &p) const {
return x != p.x;
}
Mod_Int inverse() const {
assert(*this != Mod_Int(0));
return pow(mod - 2);
}
Mod_Int pow(long long k) const {
Mod_Int now = *this, ret = 1;
for (; k > 0; k >>= 1, now *= now) {
if (k & 1)
ret *= now;
}
return ret;
}
friend ostream &operator<<(ostream &os, const Mod_Int &p) {
return os << p.x;
}
friend istream &operator>>(istream &is, Mod_Int &p) {
long long a;
is >> a;
p = Mod_Int<mod>(a);
return is;
}
};
ll mpow2(ll x, ll n, ll mod) {
ll ans = 1;
x %= mod;
while (n != 0) {
if (n & 1)
ans = ans * x % mod;
x = x * x % mod;
n = n >> 1;
}
ans %= mod;
return ans;
}
ll modinv2(ll a, ll mod) {
ll b = mod, u = 1, v = 0;
while (b) {
ll t = a / b;
a -= t * b;
swap(a, b);
u -= t * v;
swap(u, v);
}
u %= mod;
if (u < 0)
u += mod;
return u;
}
ll divide_int(ll a, ll b) {
return (a >= 0 ? a / b : (a - b + 1) / b);
}
// const int MOD = 1000000007;
const int MOD = 998244353;
using mint = Mod_Int<MOD>;
mint mpow(mint x, ll n) {
bool rev = n < 0;
n = abs(n);
mint ans = 1;
while (n != 0) {
if (n & 1)
ans *= x;
x *= x;
n = n >> 1;
}
return (rev ? ans.inverse() : ans);
}
// ----- library -------
template <typename T>
struct Number_Theoretic_Transform {
static int max_base;
static T root;
static vector<T> r, ir;
Number_Theoretic_Transform() {
}
static void init() {
if (!r.empty())
return;
int mod = T::get_mod();
int tmp = mod - 1;
root = 2;
while (root.pow(tmp >> 1) == 1)
root++;
max_base = 0;
while (tmp % 2 == 0)
tmp >>= 1, max_base++;
r.resize(max_base), ir.resize(max_base);
for (int i = 0; i < max_base; i++) {
r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i] := 1 の 2^(i+2) 乗根
ir[i] = r[i].inverse(); // ir[i] := 1/r[i]
}
}
static void ntt(vector<T> &a) {
init();
int n = a.size();
assert((n & (n - 1)) == 0);
assert(n <= (1 << max_base));
for (int k = n; k >>= 1;) {
T w = 1;
for (int s = 0, t = 0; s < n; s += 2 * k) {
for (int i = s, j = s + k; i < s + k; i++, j++) {
T x = a[i], y = w * a[j];
a[i] = x + y, a[j] = x - y;
}
w *= r[__builtin_ctz(++t)];
}
}
}
static void intt(vector<T> &a) {
init();
int n = a.size();
assert((n & (n - 1)) == 0);
assert(n <= (1 << max_base));
for (int k = 1; k < n; k <<= 1) {
T w = 1;
for (int s = 0, t = 0; s < n; s += 2 * k) {
for (int i = s, j = s + k; i < s + k; i++, j++) {
T x = a[i], y = a[j];
a[i] = x + y, a[j] = w * (x - y);
}
w *= ir[__builtin_ctz(++t)];
}
}
T inv = T(n).inverse();
for (auto &e : a)
e *= inv;
}
static vector<T> convolve(vector<T> a, vector<T> b) {
if (a.empty() || b.empty())
return {};
int k = (int)a.size() + (int)b.size() - 1, n = 1;
while (n < k)
n <<= 1;
a.resize(n), b.resize(n);
ntt(a), ntt(b);
for (int i = 0; i < n; i++)
a[i] *= b[i];
intt(a), a.resize(k);
return a;
}
};
template <typename T>
int Number_Theoretic_Transform<T>::max_base = 0;
template <typename T>
T Number_Theoretic_Transform<T>::root = T();
template <typename T>
vector<T> Number_Theoretic_Transform<T>::r = vector<T>();
template <typename T>
vector<T> Number_Theoretic_Transform<T>::ir = vector<T>();
template <typename T>
struct Formal_Power_Series : vector<T> {
using NTT_ = Number_Theoretic_Transform<T>;
using vector<T>::vector;
Formal_Power_Series(const vector<T> &v) : vector<T>(v) {
}
Formal_Power_Series pre(int n) const {
return Formal_Power_Series(begin(*this), begin(*this) + min((int)this->size(), n));
}
Formal_Power_Series rev(int deg = -1) const {
Formal_Power_Series ret = *this;
if (deg != -1)
ret.resize(deg, T(0));
reverse(begin(ret), end(ret));
return ret;
}
void normalize() {
while (!this->empty() && this->back() == 0)
this->pop_back();
}
Formal_Power_Series operator-() const {
Formal_Power_Series ret = *this;
for (int i = 0; i < (int)ret.size(); i++)
ret[i] = -ret[i];
return ret;
}
Formal_Power_Series &operator+=(const T &x) {
if (this->empty())
this->resize(1);
(*this)[0] += x;
return *this;
}
Formal_Power_Series &operator+=(const Formal_Power_Series &v) {
if (v.size() > this->size())
this->resize(v.size());
for (int i = 0; i < (int)v.size(); i++)
(*this)[i] += v[i];
this->normalize();
return *this;
}
Formal_Power_Series &operator-=(const T &x) {
if (this->empty())
this->resize(1);
*this[0] -= x;
return *this;
}
Formal_Power_Series &operator-=(const Formal_Power_Series &v) {
if (v.size() > this->size())
this->resize(v.size());
for (int i = 0; i < (int)v.size(); i++)
(*this)[i] -= v[i];
this->normalize();
return *this;
}
Formal_Power_Series &operator*=(const T &x) {
for (int i = 0; i < (int)this->size(); i++)
(*this)[i] *= x;
return *this;
}
Formal_Power_Series &operator*=(const Formal_Power_Series &v) {
if (this->empty() || empty(v)) {
this->clear();
return *this;
}
return *this = NTT_::convolve(*this, v);
}
Formal_Power_Series &operator/=(const T &x) {
assert(x != 0);
T inv = x.inverse();
for (int i = 0; i < (int)this->size(); i++)
(*this)[i] *= inv;
return *this;
}
Formal_Power_Series &operator/=(const Formal_Power_Series &v) {
if (v.size() > this->size()) {
this->clear();
return *this;
}
int n = this->size() - (int)v.size() + 1;
return *this = (rev().pre(n) * v.rev().inv(n)).pre(n).rev(n);
}
Formal_Power_Series &operator%=(const Formal_Power_Series &v) {
return *this -= (*this / v) * v;
}
Formal_Power_Series &operator<<=(int x) {
Formal_Power_Series ret(x, 0);
ret.insert(end(ret), begin(*this), end(*this));
return *this = ret;
}
Formal_Power_Series &operator>>=(int x) {
Formal_Power_Series ret;
ret.insert(end(ret), begin(*this) + x, end(*this));
return *this = ret;
}
Formal_Power_Series operator+(const T &x) const {
return Formal_Power_Series(*this) += x;
}
Formal_Power_Series operator+(const Formal_Power_Series &v) const {
return Formal_Power_Series(*this) += v;
}
Formal_Power_Series operator-(const T &x) const {
return Formal_Power_Series(*this) -= x;
}
Formal_Power_Series operator-(const Formal_Power_Series &v) const {
return Formal_Power_Series(*this) -= v;
}
Formal_Power_Series operator*(const T &x) const {
return Formal_Power_Series(*this) *= x;
}
Formal_Power_Series operator*(const Formal_Power_Series &v) const {
return Formal_Power_Series(*this) *= v;
}
Formal_Power_Series operator/(const T &x) const {
return Formal_Power_Series(*this) /= x;
}
Formal_Power_Series operator/(const Formal_Power_Series &v) const {
return Formal_Power_Series(*this) /= v;
}
Formal_Power_Series operator%(const Formal_Power_Series &v) const {
return Formal_Power_Series(*this) %= v;
}
Formal_Power_Series operator<<(int x) const {
return Formal_Power_Series(*this) <<= x;
}
Formal_Power_Series operator>>(int x) const {
return Formal_Power_Series(*this) >>= x;
}
T val(const T &x) const {
T ret = 0;
for (int i = (int)this->size() - 1; i >= 0; i--)
ret *= x, ret += (*this)[i];
return ret;
}
Formal_Power_Series diff() const { // df/dx
int n = this->size();
Formal_Power_Series ret(n - 1);
for (int i = 1; i < n; i++)
ret[i - 1] = (*this)[i] * i;
return ret;
}
Formal_Power_Series integral() const { // ∫f(x)dx
int n = this->size();
Formal_Power_Series ret(n + 1);
for (int i = 0; i < n; i++)
ret[i + 1] = (*this)[i] / (i + 1);
return ret;
}
Formal_Power_Series inv(int deg) const { // 1/f(x) (f[0] != 0)
assert((*this)[0] != T(0));
Formal_Power_Series ret(1, (*this)[0].inverse());
for (int i = 1; i < deg; i <<= 1) {
Formal_Power_Series f = pre(2 * i), g = ret;
f.resize(2 * i), g.resize(2 * i);
NTT_::ntt(f), NTT_::ntt(g);
Formal_Power_Series h(2 * i);
for (int j = 0; j < 2 * i; j++)
h[j] = f[j] * g[j];
NTT_::intt(h);
for (int j = 0; j < i; j++)
h[j] = 0;
NTT_::ntt(h);
for (int j = 0; j < 2 * i; j++)
h[j] *= g[j];
NTT_::intt(h);
for (int j = 0; j < i; j++)
h[j] = 0;
ret -= h;
}
ret.resize(deg);
return ret;
}
Formal_Power_Series inv() const {
return inv(this->size());
}
Formal_Power_Series log(int deg) const { // log(f(x)) (f[0] = 1)
assert((*this)[0] == 1);
Formal_Power_Series ret = (diff() * inv(deg)).pre(deg - 1).integral();
ret.resize(deg);
return ret;
}
Formal_Power_Series log() const {
return log(this->size());
}
Formal_Power_Series exp(int deg) const { // exp(f(x)) (f[0] = 0)
assert((*this)[0] == 0);
Formal_Power_Series inv;
inv.reserve(deg + 1);
inv.push_back(0), inv.push_back(1);
auto inplace_integral = [&](Formal_Power_Series &F) -> void {
int n = F.size();
int mod = T::get_mod();
while ((int)inv.size() <= n) {
int i = inv.size();
inv.push_back((-inv[mod % i]) * (mod / i));
}
F.insert(begin(F), 0);
for (int i = 1; i <= n; i++)
F[i] *= inv[i];
};
auto inplace_diff = [](Formal_Power_Series &F) -> void {
if (F.empty())
return;
F.erase(begin(F));
T coeff = 1, one = 1;
for (int i = 0; i < (int)F.size(); i++) {
F[i] *= coeff;
coeff += one;
}
};
Formal_Power_Series ret{1, this->size() > 1 ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
for (int m = 2; m < deg; m *= 2) {
auto y = ret;
y.resize(2 * m);
NTT_::ntt(y);
z1 = z2;
Formal_Power_Series z(m);
for (int i = 0; i < m; i++)
z[i] = y[i] * z1[i];
NTT_::intt(z);
fill(begin(z), begin(z) + m / 2, 0);
NTT_::ntt(z);
for (int i = 0; i < m; i++)
z[i] *= -z1[i];
NTT_::intt(z);
c.insert(end(c), begin(z) + m / 2, end(z));
z2 = c, z2.resize(2 * m);
NTT_::ntt(z2);
Formal_Power_Series x(begin(*this), begin(*this) + min((int)this->size(), m));
inplace_diff(x);
x.push_back(0);
NTT_::ntt(x);
for (int i = 0; i < m; i++)
x[i] *= y[i];
NTT_::intt(x);
x -= ret.diff(), x.resize(2 * m);
for (int i = 0; i < m - 1; i++)
x[m + i] = x[i], x[i] = 0;
NTT_::ntt(x);
for (int i = 0; i < 2 * m; i++)
x[i] *= z2[i];
NTT_::intt(x);
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, 0);
NTT_::ntt(x);
for (int i = 0; i < 2 * m; i++)
x[i] *= y[i];
NTT_::intt(x);
ret.insert(end(ret), begin(x) + m, end(x));
}
ret.resize(deg);
return ret;
}
Formal_Power_Series exp() const {
return exp(this->size());
}
Formal_Power_Series pow(long long k, int deg) const { // f(x)^k
int n = this->size();
for (int i = 0; i < n; i++) {
if ((*this)[i] == 0)
continue;
T rev = (*this)[i].inverse();
Formal_Power_Series C(*this * rev), D(n - i, 0);
for (int j = i; j < n; j++)
D[j - i] = C[j];
D = (D.log() * k).exp() * ((*this)[i].pow(k));
Formal_Power_Series E(deg, 0);
if (i > 0 && k > deg / i)
return E;
long long S = i * k;
for (int j = 0; j + S < deg && j < D.size(); j++)
E[j + S] = D[j];
E.resize(deg);
return E;
}
return Formal_Power_Series(deg, 0);
}
Formal_Power_Series pow(long long k) const {
return pow(k, this->size());
}
Formal_Power_Series Taylor_shift(T c) const { // f(x+c)
int n = this->size();
vector<T> ifac(n, 1);
Formal_Power_Series f(n), g(n);
for (int i = 0; i < n; i++) {
f[n - 1 - i] = (*this)[i] * ifac[n - 1];
if (i < n - 1)
ifac[n - 1] *= i + 1;
}
ifac[n - 1] = ifac[n - 1].inverse();
for (int i = n - 1; i > 0; i--)
ifac[i - 1] = ifac[i] * i;
T pw = 1;
for (int i = 0; i < n; i++) {
g[i] = pw * ifac[i];
pw *= c;
}
f *= g;
Formal_Power_Series b(n);
for (int i = 0; i < n; i++)
b[i] = f[n - 1 - i] * ifac[i];
return b;
}
};
using FPS = Formal_Power_Series<mint>;
template <typename T>
struct Combination {
vector<T> _fac, _ifac;
Combination() {
init();
}
Combination(int n) {
init(n);
}
void init(int n = 2000010) {
_fac.resize(n + 1), _ifac.resize(n + 1);
_fac[0] = 1;
for (int i = 1; i <= n; i++)
_fac[i] = _fac[i - 1] * i;
_ifac[n] = _fac[n].inverse();
for (int i = n; i >= 1; i--)
_ifac[i - 1] = _ifac[i] * i;
}
T fac(int k) {
return _fac[k];
}
T ifac(int k) {
return _ifac[k];
}
T inv(int k) {
return fac(k - 1) * ifac(k);
}
T P(int n, int k) {
if (k < 0 || n < k)
return 0;
return fac(n) * ifac(n - k);
}
T C(int n, int k) {
if (k < 0 || n < k)
return 0;
return fac(n) * ifac(n - k) * ifac(k);
}
T H(int n, int k) { // k個の区別できない玉をn個の区別できる箱に入れる場合の数
if (n < 0 || k < 0)
return 0;
return k == 0 ? 1 : C(n + k - 1, k);
}
T second_stirling_number(int n, int k) { // n個の区別できる玉を、k個の区別しない箱に、各箱に1個以上玉が入るように入れる場合の数
T ret = 0;
for (int i = 0; i <= k; i++) {
T tmp = C(k, i) * T(i).pow(n);
ret += ((k - i) & 1) ? -tmp : tmp;
}
return ret * ifac(k);
}
T bell_number(int n, int k) { // n個の区別できる玉を、k個の区別しない箱に入れる場合の数
if (n == 0)
return 1;
k = min(k, n);
vector<T> pref(k + 1);
pref[0] = 1;
for (int i = 1; i <= k; i++) {
if (i & 1)
pref[i] = pref[i - 1] - ifac(i);
else
pref[i] = pref[i - 1] + ifac(i);
}
T ret = 0;
for (int i = 1; i <= k; i++)
ret += T(i).pow(n) * ifac(i) * pref[k - i];
return ret;
}
};
using comb = Combination<mint>;
// ----- library -------
int main() {
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
cout << fixed << setprecision(15);
int n;
cin >> n;
vector<int> a(n);
rep(i, n) cin >> a[i];
mint ans = 0;
rep(i, n) ans += mpow(2, n - 1) * a[i];
int sum = accumulate(all(a), 0) - 999630629;
if (sum >= 0) {
vector<int> c(sum + 1, 0);
rep(i, n) if (a[i] <= sum) c[a[i]]++;
comb comb;
FPS f(sum + 1, 0);
rep2(i, 1, sum + 1) {
for (int j = 1; j * i <= sum; j++) {
mint tmp = mint(j).inverse() * c[i];
f[j * i] += (j & 1 ? tmp : -tmp);
}
}
f = f.exp();
rep(i, sum + 1) ans -= f[i] * 999630629;
}
cout << ans << endl;
}