結果

問題 No.2062 Sum of Subset mod 999630629
ユーザー fumofumofuni
提出日時 2022-08-27 00:55:36
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
CE  
(最新)
AC  
(最初)
実行時間 -
コード長 24,809 bytes
コンパイル時間 7,304 ms
コンパイル使用メモリ 290,844 KB
最終ジャッジ日時 2025-01-31 06:02:59
ジャッジサーバーID
(参考情報)
judge2 / judge4
このコードへのチャレンジ
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コンパイルエラー時のメッセージ・ソースコードは、提出者また管理者しか表示できないようにしております。(リジャッジ後のコンパイルエラーは公開されます)
ただし、clay言語の場合は開発者のデバッグのため、公開されます。

コンパイルメッセージ
main.cpp: In function 'FPS log(const FPS&, int)':
main.cpp:523:24: error: expected 'auto' or 'decltype(auto)' after 'integral'
  523 |                 return integral((derivative(f) * f.inv(d - 1)).resize(d - 1));
      |                        ^~~~~~~~
main.cpp:523:24: error: 'auto(x)' cannot be constrained
  523 |                 return integral((derivative(f) * f.inv(d - 1)).resize(d - 1));
      |                        ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

ソースコード

diff #
プレゼンテーションモードにする

#ifndef HIDDEN_IN_VISUAL_STUDIO //
//
#define _CRT_SECURE_NO_WARNINGS
// 使
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; // -2^63 2^63 = 9 * 10^18int -2^31 2^31 = 2 * 10^9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = 3.14159265359;
const double DEG = PI / 180.; // θ [deg] = θ * DEG [rad]
const vi dx4 = { 1, 0, -1, 0 }; // 4
const vi dy4 = { 0, 1, 0, -1 };
const vi dx8 = { 1, 1, 0, -1, -1, -1, 0, 1 }; // 8
const vi dy8 = { 0, 1, 1, 1, 0, -1, -1, -1 };
const ll INFL = (ll)2e18; const int INF = (int)1e9;
const double EPS = 1e-10; // 調
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define distance (int)distance
#define Yes(b) {cout << ((b) ? "Yes" : "No") << endl;}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define repit(it, a) for(auto it = (a).begin(); it != (a).end(); ++it) //
#define repitr(it, a) for(auto it = (a).rbegin(); it != (a).rend(); ++it) //
//
template <class T> inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
// >>, <<
template <class T, class U> inline istream& operator>> (istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T, class U> inline ostream& operator<< (ostream& os, const pair<T, U>& p) { os << "(" << p.first << "," << p.second << ")"; return os
    ; }
template <class T, class U, class V> inline istream& operator>> (istream& is, tuple<T, U, V>& t) { is >> get<0>(t) >> get<1>(t) >> get<2>(t); return
    is; }
template <class T, class U, class V> inline ostream& operator<< (ostream& os, const tuple<T, U, V>& t) { os << "(" << get<0>(t) << "," << get<1>(t)
    << "," << get<2>(t) << ")"; return os; }
template <class T, class U, class V, class W> inline istream& operator>> (istream& is, tuple<T, U, V, W>& t) { is >> get<0>(t) >> get<1>(t) >> get<2
    >(t) >> get<3>(t); return is; }
template <class T, class U, class V, class W> inline ostream& operator<< (ostream& os, const tuple<T, U, V, W>& t) { os << "(" << get<0>(t) << "," <<
    get<1>(t) << "," << get<2>(t) << "," << get<3>(t) << ")"; return os; }
template <class T> inline istream& operator>> (istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline ostream& operator<< (ostream& os, const vector<T>& v) { repe(x, v) os << x << " "; return os; }
template <class T> inline ostream& operator<< (ostream& os, const set<T>& s) { repe(x, s) os << x << " "; return os; }
template <class T> inline ostream& operator<< (ostream& os, const unordered_set<T>& s) { repe(x, s) os << x << " "; return os; }
template <class T, class U> inline ostream& operator<< (ostream& os, const map<T, U>& m) { repe(p, m) os << p << " "; return os; }
template <class T, class U> inline ostream& operator<< (ostream& os, const unordered_map<T, U>& m) { repe(p, m) os << p << " "; return os; }
template <class T> inline ostream& operator<< (ostream& os, stack<T> s) { while (!s.empty()) { os << s.top() << " "; s.pop(); } return os; }
template <class T> inline ostream& operator<< (ostream& os, queue<T> q) { while (!q.empty()) { os << q.front() << " "; q.pop(); } return os; }
template <class T> inline ostream& operator<< (ostream& os, deque<T> q) { while (!q.empty()) { os << q.front() << " "; q.pop_front(); } return os; }
template <class T> inline ostream& operator<< (ostream& os, priority_queue<T> q) { while (!q.empty()) { os << q.top() << " "; q.pop(); } return os; }
// Visual Studio
#ifdef _MSC_VER
#define popcount (int)__popcnt // 1
#define popcountll (int)__popcnt64
inline int lsb(unsigned int n) { unsigned long i; _BitScanForward(&i, n); return i; } // 0-indexed
inline int lsbll(unsigned long long n) { unsigned long i; _BitScanForward64(&i, n); return i; }
inline int msb(unsigned int n) { unsigned long i; _BitScanReverse(&i, n); return i; } // 0-indexed
inline int msbll(unsigned long long n) { unsigned long i; _BitScanReverse64(&i, n); return i; }
template <class T> T gcd(T a, T b) { return b ? gcd(b, a % b) : a; }
#define dump(x) cout << "\033[1;36m" << (x) << "\033[0m" << endl;
#define dumps(x) cout << "\033[1;36m" << (x) << "\033[0m ";
#define dumpel(a) { int i = 0; cout << "\033[1;36m"; repe(x, a) {cout << i++ << ": " << x << endl;} cout << "\033[0m"; }
#define input_from_file(f) ifstream isTMP(f); cin.rdbuf(isTMP.rdbuf());
#define output_to_file(f) ofstream osTMP(f); cout.rdbuf(osTMP.rdbuf());
// gcc
#else
#define popcount (int)__builtin_popcount
#define popcountll (int)__builtin_popcountll
#define lsb __builtin_ctz
#define lsbll __builtin_ctzll
#define msb(n) (31 - __builtin_clz(n))
#define msbll(n) (63 - __builtin_clzll(n))
#define gcd __gcd
#define dump(x)
#define dumps(x)
#define dumpel(v)
#define input_from_file(f)
#define output_to_file(f)
#endif
#endif //
//-----------------AtCoder -----------------
#include <atcoder/all>
using namespace atcoder;
//using mint = modint1000000007;
using mint = modint998244353;
//using mint = modint; // mint::set_mod(m);
template <class S, S(*op)(S, S), S(*e)()>ostream& operator<<(ostream& os, segtree<S, op, e> seg) { int n = seg.max_right(0, [](S x) {return true; });
    rep(i, n) os << seg.get(i) << " "; return os; }
template <class S, S(*op)(S, S), S(*e)(), class F, S(*mp)(F, S), F(*cp)(F, F), F(*id)()>ostream& operator<<(ostream& os, lazy_segtree<S, op, e, F, mp
    , cp, id> seg) { int n = seg.max_right(0, [](S x) {return true; }); rep(i, n) os << seg.get(i) << " "; return os; }
istream& operator>> (istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
ostream& operator<< (ostream& os, const mint& x) { os << x.val(); return os; }
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>;
//----------------------------------------------
//
/*
* mod 998244353 O(n^2)
*
* FPS() : O(1)
* f = 0
*
* FPS(c0) : O(1)
* f = c0
*
* FPS(c0, d) : O(d)
* d f = c0
*
* FPS(c) : O(|c|)
* f(x) = c[0] + c[1] x + ... + c[n - 1] x^(n-1)
*
* c + f, f + c : O(1) f + g : O(n)
* f - c : O(1) c - f, f - g, -f : O(n)
* c * f, f * c : O(n) f * g : O(n log n) f * g_sp : O(n k)k : g
* f / c : O(n) f / g : O(n log n) f / g_sp : O(n k)k : g
*
* g_sp {, } vector
* : g(0) ≠ 0
*
* f.inv(d) : O(n log n)
* 1 / f mod x^d
* : f(0) ≠ 0
*
* f.quotient(g) : O(n log n)
* f.reminder(g) : O(n log n)
* f.quotient_remainder(g) : O(n log n)
* f g
*
* f.pow(k, d) : O(n log n)
* f(x)^k mod x^d
*
* f.deg(), f.size() : O(1)
* f [+1]
*
* FPS::monomial(d) : O(d)
* x^d
*
* f.assign(c) : O(n)
* f x c
*
* f.resize(d) : O(1)
* mod x^d
*
* f.resize() : O(n)
*
*
* f >> d, f << d : O(n)
* d []
* x^d x^d
*
* power_mod(f, d, g) : O(m log m log d) m = deg g
* f(x)^d % g(x)
*
* derivative(f) : O(n)
* f'(x)
*
* integral(f) : O(n)
* ∫ f(x) dx 0
*
* log(f, d) : O(n log n)
* log f(x) mod x^d
* : f(0) = 1
*
* exp(f, d) : O(n log n)
* exp f(x) mod x^d
* : f(0) = 0;
*/
struct FPS {
using SFPS = vector<pair<int, mint>>;
int n; // + 1
vm c; //
// 0
FPS() : n(0) {}
FPS(const mint& c0) : n(1), c({ c0 }) {}
FPS(const int& c0) : n(1), c({ mint(c0) }) {}
FPS(const mint& c0, int d) : n(d), c(n) { c[0] = c0; }
FPS(const int& c0, int d) : n(d), c(n) { c[0] = c0; }
FPS(const vm& c_) : n(sz(c_)), c(c_) {}
FPS(const vi& c_) : n(sz(c_)), c(n) { rep(i, n) c[i] = c_[i]; }
//
FPS(const FPS& f) = default;
FPS& operator=(const FPS& f) = default;
FPS& operator=(const mint& c0) { n = 1; c = { c0 }; return *this; }
//
mint const& operator[](int i) const { return c[i]; }
mint& operator[](int i) { return c[i]; }
//
int deg() const { return n - 1; }
int size() const { return n; }
//
FPS& operator+=(const FPS& g) {
if (n >= g.n) rep(i, g.n) c[i] += g.c[i];
else {
rep(i, n) c[i] += g.c[i];
repi(i, n, g.n - 1) c.push_back(g.c[i]);
n = g.n;
}
return *this;
}
FPS operator+(const FPS& g) const { return FPS(*this) += g; }
//
FPS& operator+=(const mint& sc) {
if (n == 0) { n = 1; c = { sc }; }
else { c[0] += sc; }
return *this;
}
FPS operator+(const mint& sc) const { return FPS(*this) += sc; }
friend FPS operator+(const mint& sc, const FPS& f) { return f + sc; }
FPS& operator+=(const int& sc) { *this += mint(sc); return *this; }
FPS operator+(const int& sc) const { return FPS(*this) += sc; }
friend FPS operator+(const int& sc, const FPS& f) { return f + sc; }
//
FPS& operator-=(const FPS& g) {
if (n >= g.n) rep(i, g.n) c[i] -= g.c[i];
else {
rep(i, n) c[i] -= g.c[i];
repi(i, n, g.n - 1) c.push_back(-g.c[i]);
n = g.n;
}
return *this;
}
FPS operator-(const FPS& g) const { return FPS(*this) -= g; }
//
FPS& operator-=(const mint& sc) { *this += -sc; return *this; }
FPS operator-(const mint& sc) const { return FPS(*this) -= sc; }
friend FPS operator-(const mint& sc, const FPS& f) { return -(f - sc); }
FPS& operator-=(const int& sc) { *this += -sc; return *this; }
FPS operator-(const int& sc) const { return FPS(*this) -= sc; }
friend FPS operator-(const int& sc, const FPS& f) { return -(f - sc); }
//
FPS operator-() const { return FPS(*this) *= -1; }
//
FPS& operator*=(const mint& sc) { rep(i, n) c[i] *= sc; return *this; }
FPS operator*(const mint& sc) const { return FPS(*this) *= sc; }
friend FPS operator*(const mint& sc, const FPS& f) { return f * sc; }
FPS& operator*=(const int& sc) { *this *= mint(sc); return *this; }
FPS operator*(const int& sc) const { return FPS(*this) *= sc; }
friend FPS operator*(const int& sc, const FPS& f) { return f * sc; }
//
FPS& operator/=(const mint& sc) { *this *= sc.inv(); return *this; }
FPS operator/(const mint& sc) const { return FPS(*this) /= sc; }
FPS& operator/=(const int& sc) { *this /= mint(sc); return *this; }
FPS operator/(const int& sc) const { return FPS(*this) /= sc; }
//
FPS& operator*=(const FPS& g) {
if (mint::mod() == 998244353) return mul998244353(g);
else return mul_other(g);
}
FPS& mul998244353(const FPS& g) { c = convolution(c, g.c); n = sz(c); return *this; }
FPS& mul_other(const FPS& g) {
int m = g.deg();
resize(n + m);
// DP
repir(i, n - 1, 0) {
//
repi(j, 1, m) {
if (i + j >= n) break;
c[(ll)i + j] += c[i] * g[j];
}
//
c[i] *= g[0];
}
return *this;
}
FPS operator*(const FPS& g) const { return FPS(*this) *= g; }
//
FPS inv(int d) const {
// https://nyaannyaan.github.io/library/fps/formal-power-series.hpp
//
// 1 / f mod x^d
// f g = 1 (mod x^d)
// g
// d 1, 2, 4, ..., 2^i
//
// d = 1
// g = 1 / f[0] (mod x^1)
//
//
//
// g = h (mod x^k)
//
// g mod x^(2 k)
//
// g - h = 0 (mod x^k)
// ⇒ (g - h)^2 = 0 (mod x^(2 k))
// ⇔ g^2 - 2 g h + h^2 = 0 (mod x^(2 k))
// ⇒ f g^2 - 2 f g h + f h^2 = 0 (mod x^(2 k))
// ⇔ g - 2 h + f h^2 = 0 (mod x^(2 k))  (f g = 1 (mod x^d) )
// ⇔ g = (2 - f h) h (mod x^(2 k))
//
//
// d <= 2^i i d
FPS g(c[0].inv());
for (int k = 1; k < d; k *= 2) {
g = (2 - *this * g) * g;
g.resize(2 * k);
}
return g.resize(d);
}
FPS& operator/=(const FPS& g) { return *this *= g.inv(n); }
FPS operator/(const FPS& g) const { return FPS(*this) /= g; }
//
FPS quotient(const FPS& g) const {
// : https://nyaannyaan.github.io/library/fps/formal-power-series.hpp
//
// f(x) = g(x) q(x) + r(x) q(x)
// f n - 1, g m - 1 (n >= m)
// q n - mr m - 2
//
// f^R f
// f^R(x) := f(1/x) x^(n-1)
//
//
// x → 1/x
// f(1/x) = g(1/x) q(1/x) + r(1/x)
// ⇔ f(1/x) x^(n-1) = g(1/x) q(1/x) x^(n-1) + r(1/x) x^(n-1)
// ⇔ f(1/x) x^(n-1) = g(1/x) x^(m-1) q(1/x) x^(n-m) + r(1/x) x^(m-2) x^(n-m+1)
// ⇔ f^R(x) = g^R(x) q^R(x) + r^R(x) x^(n-m+1)
// ⇒ f^R(x) = g^R(x) q^R(x) (mod x^(n-m+1))
// ⇒ q^R(x) = f^R(x) / g^R(x) (mod x^(n-m+1))
//
//
// q mod x^(n-m+1)
// q n - m q
if (n < g.n) return FPS();
return ((this->rev() / g.rev()).resize(n - g.n + 1)).rev();
}
FPS reminder(const FPS& g) const { return (*this - this->quotient(g) * g).resize(g.n - 1); }
pair<FPS, FPS> quotient_remainder(const FPS& g) const {
pair<FPS, FPS> res;
res.first = this->quotient(g);
res.second = (*this - res.first * g).resize(g.n - 1);
return res;
}
//
FPS& operator*=(const SFPS& g) {
// g
auto it0 = g.begin();
mint g0 = 0;
if (it0->first == 0) {
g0 = it0->second;
it0++;
}
// DP
repir(i, n - 1, 0) {
//
for (auto it = it0; it != g.end(); it++) {
int j; mint gj;
tie(j, gj) = *it;
if (i + j >= n) break;
c[(ll)i + j] += c[i] * gj;
}
//
c[i] *= g0;
}
return *this;
}
FPS operator*(const SFPS& g) const { return FPS(*this) *= g; }
//
FPS& operator/=(const SFPS& g) {
// g
auto it0 = g.begin();
assert(it0->first == 0 && it0->second != 0);
mint g0_inv = it0->second.inv();
it0++;
// DP
rep(i, n) {
//
c[i] *= g0_inv;
//
for (auto it = it0; it != g.end(); it++) {
int j; mint gj;
tie(j, gj) = *it;
if (i + j >= n) break;
c[(ll)i + j] -= c[i] * gj;
}
}
return *this;
}
FPS operator/(const SFPS& g) const { return FPS(*this) /= g; }
//
FPS rev() const { FPS h = *this; reverse(all(h.c)); return h; }
//
friend FPS monomial(int d) {
FPS mono(0, d + 1);
mono[d] = 1;
return mono;
}
//
FPS& resize() {
// 0
while (n > 0 && c[n - 1LL] == 0) {
c.pop_back();
n--;
}
return *this;
}
//
FPS& resize(int d) {
// x^d
n = d;
c.resize(d);
return *this;
}
//
mint assign(const mint& x) const {
mint val = 0;
repir(i, n - 1, 0) val = val * x + c[i];
return val;
}
//
FPS& operator>>=(int d) {
n += d;
c.insert(c.begin(), d, 0);
return *this;
}
FPS& operator<<=(int d) {
n -= d;
if (n <= 0) { c.clear(); n = 0; }
else c.erase(c.begin(), c.begin() + d);
return *this;
}
FPS operator>>(int d) const { return FPS(*this) >>= d; }
FPS operator<<(int d) const { return FPS(*this) <<= d; }
//
friend FPS power_mod(const FPS& f, ll d, const FPS& g) {
FPS res(1), pow2(f);
while (d > 0) {
if (d & 1) res = (res * pow2).reminder(g);
pow2 = (pow2 * pow2).reminder(g);
d /= 2;
}
return res;
}
//
friend FPS derivative(const FPS& f) {
FPS res;
repi(i, 1, f.n - 1) res.c.push_back(f[i] * i);
res.n = sz(res.c);
return res;
}
//
friend FPS integral(const FPS& f) {
FPS res(0);
repi(i, 0, f.n - 1) res.c.push_back(f[i] / (i + 1));
res.n = sz(res.c);
return res;
}
//
friend FPS log(const FPS& f, int d) {
// : https://qiita.com/hotman78/items/f0e6d2265badd84d429a
return integral((derivative(f) * f.inv(d - 1)).resize(d - 1));
}
//
friend FPS exp(const FPS& f, int d) {
// : https://qiita.com/hotman78/items/f0e6d2265badd84d429a
//
// g(x) = exp(f(x))
// log g(x) = f(x)
//
//
// f(0) = 0 mod x^1
// log(1) ≡ f(x) mod x^1
//
//
// mod x^k
// log h(x) ≡ f(x) mod x^k
//
// g = h - (log h - f) / (log h)'
// ⇔ g = h (f + 1 - log h)
//
// log g(x) ≡ f(x) mod x^(2 k)
//
//
// g
// log g = f g
FPS g(1);
for (int k = 1; k < d; k *= 2) {
g = g * (f + 1 - log(g, 2 * k));
g.resize(2 * k);
}
g.resize(d);
return g;
}
//
FPS pow(ll k, int d) const {
// : https://qiita.com/hotman78/items/f0e6d2265badd84d429a
//
int i0 = 0;
while (i0 < n && c[i0] == 0) i0++;
// f = 0 f^k = 0
if (i0 == n) return FPS(0, d);
//
mint c0 = c[i0];
// 1
FPS fs = (*this << i0) / c0;
ll ds = d - k * i0;
// k * i0 0
if (ds <= 0) return FPS(0, d);
// f^k = exp(k log f(x)) f^k
FPS gs = exp(mint(k) * log(fs, (int)ds), (int)ds);
//
FPS g = (gs * c0.pow(k)) >> ((int)k * i0);
return g;
}
//
friend ostream& operator<<(ostream& os, const FPS& f) {
if (f.n == 0) os << 0;
else {
rep(i, f.n) {
os << f[i].val() << "x^" << i;
if (i < f.n - 1) os << " + ";
}
}
return os;
}
};
//mint
/*
*
*
* factorial_mint(n) : O(n)
* n!
*
* fac(n) : O(1)
* n!
*
* fac_inv(n) : O(1)
* 1 / n!
*
* inv(n) : O(1)
* 1 / n
*
* nPr(n, r) : O(1)
* nPr
*
* nCr(n, r) : O(1)
* nCr
*
* nCr(r) : O(|r|)
* nC[r] n = Σr
*/
struct factorial_mint {
//
int n_;
vm fac_, fac_inv_, inv_;
// n! O(n)
factorial_mint(int n) : n_(n) {
fac_ = vm(n + 1LL);
fac_[0] = 1;
repi(i, 1, n) fac_[i] = fac_[i - 1LL] * i;
fac_inv_ = vm(n + 1LL);
fac_inv_[n] = fac_[n].inv();
repir(i, n - 1, 1) fac_inv_[i] = fac_inv_[i + 1LL] * (i + 1);
fac_inv_[0] = 1;
inv_ = vm(n + 1LL);
repi(i, 1, n) inv_[i] = fac_[i - 1LL] * fac_inv_[i];
}
// n! O(1)
mint fac(int n) const { assert(n <= n_); return fac_[n]; }
// 1 / n! O(1)
mint fac_inv(int n) const { assert(n <= n_); return fac_inv_[n]; }
// 1 / n O(1)
mint inv(int n) const { assert(n != 0 && n <= n_); return inv_[n]; }
// nPr O(1)
mint nPr(int n, int r) const {
assert(n <= n_);
if (r < 0 || n - r < 0) return 0;
return fac_[n] * fac_inv_[(ll)n - r];
}
// nCr O(1)
mint nCr(int n, int r) const {
assert(n <= n_);
if (r < 0 || n - r < 0) return 0;
return fac_[n] * fac_inv_[r] * fac_inv_[(ll)n - r];
}
// nC[r] O(|r|)
mint nCr(const vi& r) const {
int n = accumulate(all(r), 0);
assert(n <= n_);
mint res = fac_[n];
repe(ri, r) res *= fac_inv_[ri];
return res;
}
};
//O(n + v log v)
/*
* j=[0..v] n a j
* cnt[j]
*
* mint
*/
void count_partial_sum(const vi& a, int v, vm& cnt) {
// : https://qiita.com/hotman78/items/f0e6d2265badd84d429a
//
//
// f(x) = Πi=[0..n) (1 + x^a[i])
//
// f(x) = exp(Σi=[0..n) log(1 + x^a[i]))
//
// log(1 + x^a[i]) = Σk=[1..∞) (-1)^(k-1) 1/k x^(k * a[i])
//
factorial_mint fm(v);
unordered_map<int, int> c;
repe(x, a) c[x]++;
dumpel(c);
FPS f(0, v + 1);
repe(p, c) {
for (int k = 1; k * p.first <= v; k++) {
f[(ll)k * p.first] += p.second * (k & 1 ? 1 : -1) * fm.inv(k);
}
}
dump(f);
f = exp(f, v + 1);
dump(f);
cnt = f.c;
}
int main() {
cout << fixed << setprecision(15);
// input_from_file("input.txt");
// output_to_file("output.txt");
int n, t;
cin >> n;
vi s(n);
cin >> s;
int al=accumulate(s.begin(),s.end(),0);
t=al-999630629;
mint ans=0;
if(t>0){
vm cnt;
count_partial_sum(s, t, cnt);
repi(i, 1, t) {
ans-=999630629*cnt[i];
}
ans-=999630629;
}
cout << ans+mint(2).pow(n-1)*al << endl;
}
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