結果
| 問題 | No.2817 Competition |
| ユーザー |
👑  rin204
|
| 提出日時 | 2024-07-19 22:58:22 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 36,536 bytes |
| コンパイル時間 | 4,265 ms |
| コンパイル使用メモリ | 273,468 KB |
| 実行使用メモリ | 100,424 KB |
| 最終ジャッジ日時 | 2024-07-19 22:58:31 |
| 合計ジャッジ時間 | 7,685 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
（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
10,624 KB |
| testcase_01 | AC | 2 ms
5,376 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | TLE | - |
| testcase_04 | -- | - |
| testcase_05 | -- | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
ソースコード
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
// #define INTERACTIVE
#include <bits/stdc++.h>
using namespace std;
namespace templates {
// type
using ll = long long;
using ull = unsigned long long;
using Pii = pair<int, int>;
using Pil = pair<int, ll>;
using Pli = pair<ll, int>;
using Pll = pair<ll, ll>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
// clang-format off
#define vec(T, A, ...) vector<T> A(__VA_ARGS__);
#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));
#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));
// clang-format on
// for loop
#define fori1(a) for (ll _ = 0; _ < (a); _++)
#define fori2(i, a) for (ll i = 0; i < (a); i++)
#define fori3(i, a, b) for (ll i = (a); i < (b); i++)
#define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)
// declare and input
// clang-format off
#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);
#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);
#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);
#define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___);
#define VEC(T, A, n) vector<T> A(n); inp(A);
#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);
// clang-format on
// const value
const ll MOD1 = 1000000007;
const ll MOD9 = 998244353;
const double PI = acos(-1);
// other macro
#if !defined(RIN__LOCAL) && !defined(INTERACTIVE)
#define endl "\n"
#endif
#define spa ' '
#define len(A) ll(A.size())
#define all(A) begin(A), end(A)
// function
vector<char> stoc(string &S) {
int n = S.size();
vector<char> ret(n);
for (int i = 0; i < n; i++) ret[i] = S[i];
return ret;
}
string ctos(vector<char> &S) {
int n = S.size();
string ret = "";
for (int i = 0; i < n; i++) ret += S[i];
return ret;
}
template <class T>
auto min(const T &a) {
return *min_element(all(a));
}
template <class T>
auto max(const T &a) {
return *max_element(all(a));
}
template <class T, class S>
auto clamp(T &a, const S &l, const S &r) {
return (a > r ? r : a < l ? l : a);
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chclamp(T &a, const S &l, const S &r) {
auto b = clamp(a, l, r);
return (a != b ? a = b, 1 : 0);
}
template <typename T>
T sum(vector<T> &A) {
T tot = 0;
for (auto a : A) tot += a;
return tot;
}
template <typename T>
vector<T> compression(vector<T> X) {
sort(all(X));
X.erase(unique(all(X)), X.end());
return X;
}
// input and output
namespace io {
// __int128_t
std::ostream &operator<<(std::ostream &dest, __int128_t value) {
std::ostream::sentry s(dest);
if (s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if (dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
// vector<T>
template <typename T>
istream &operator>>(istream &is, vector<T> &A) {
for (auto &a : A) is >> a;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << ' ';
}
return os;
}
// vector<vector<T>>
template <typename T>
istream &operator>>(istream &is, vector<vector<T>> &A) {
for (auto &a : A) is >> a;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<vector<T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << endl;
}
return os;
}
// pair<S, T>
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &A) {
is >> A.first >> A.second;
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, pair<S, T> &A) {
os << A.first << ' ' << A.second;
return os;
}
// vector<pair<S, T>>
template <typename S, typename T>
istream &operator>>(istream &is, vector<pair<S, T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
is >> A[i];
}
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, vector<pair<S, T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << endl;
}
return os;
}
// tuple
template <typename T, size_t N>
struct TuplePrint {
static ostream &print(ostream &os, const T &t) {
TuplePrint<T, N - 1>::print(os, t);
os << ' ' << get<N - 1>(t);
return os;
}
};
template <typename T>
struct TuplePrint<T, 1> {
static ostream &print(ostream &os, const T &t) {
os << get<0>(t);
return os;
}
};
template <typename... Args>
ostream &operator<<(ostream &os, const tuple<Args...> &t) {
TuplePrint<decltype(t), sizeof...(Args)>::print(os, t);
return os;
}
// io functions
void FLUSH() {
cout << flush;
}
void print() {
cout << endl;
}
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
cout << head;
if (sizeof...(Tail)) cout << spa;
print(std::forward<Tail>(tail)...);
}
template <typename T, typename S>
void prisep(vector<T> &A, S sep) {
int n = A.size();
for (int i = 0; i < n; i++) {
cout << A[i];
if (i != n - 1) cout << sep;
}
cout << endl;
}
template <typename T, typename S>
void priend(T A, S end) {
cout << A << end;
}
template <typename T>
void prispa(T A) {
priend(A, spa);
}
template <typename T, typename S>
bool printif(bool f, T A, S B) {
if (f)
print(A);
else
print(B);
return f;
}
template <class... T>
void inp(T &...a) {
(cin >> ... >> a);
}
} // namespace io
using namespace io;
// read graph
vector<vector<int>> read_edges(int n, int m, bool direct = false, int indexed = 1) {
vector<vector<int>> edges(n, vector<int>());
for (int i = 0; i < m; i++) {
INT(u, v);
u -= indexed;
v -= indexed;
edges[u].push_back(v);
if (!direct) edges[v].push_back(u);
}
return edges;
}
vector<vector<int>> read_tree(int n, int indexed = 1) {
return read_edges(n, n - 1, false, indexed);
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wedges(int n, int m, bool direct = false, int indexed = 1) {
vector<vector<pair<int, T>>> edges(n, vector<pair<int, T>>());
for (int i = 0; i < m; i++) {
INT(u, v);
T w;
inp(w);
u -= indexed;
v -= indexed;
edges[u].push_back({v, w});
if (!direct) edges[v].push_back({u, w});
}
return edges;
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wtree(int n, int indexed = 1) {
return read_wedges<T>(n, n - 1, false, indexed);
}
// yes / no
namespace yesno {
// yes
inline bool yes(bool f = true) {
cout << (f ? "yes" : "no") << endl;
return f;
}
inline bool Yes(bool f = true) {
cout << (f ? "Yes" : "No") << endl;
return f;
}
inline bool YES(bool f = true) {
cout << (f ? "YES" : "NO") << endl;
return f;
}
// no
inline bool no(bool f = true) {
cout << (!f ? "yes" : "no") << endl;
return f;
}
inline bool No(bool f = true) {
cout << (!f ? "Yes" : "No") << endl;
return f;
}
inline bool NO(bool f = true) {
cout << (!f ? "YES" : "NO") << endl;
return f;
}
// possible
inline bool possible(bool f = true) {
cout << (f ? "possible" : "impossible") << endl;
return f;
}
inline bool Possible(bool f = true) {
cout << (f ? "Possible" : "Impossible") << endl;
return f;
}
inline bool POSSIBLE(bool f = true) {
cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
return f;
}
// impossible
inline bool impossible(bool f = true) {
cout << (!f ? "possible" : "impossible") << endl;
return f;
}
inline bool Impossible(bool f = true) {
cout << (!f ? "Possible" : "Impossible") << endl;
return f;
}
inline bool IMPOSSIBLE(bool f = true) {
cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
return f;
}
// Alice Bob
inline bool Alice(bool f = true) {
cout << (f ? "Alice" : "Bob") << endl;
return f;
}
inline bool Bob(bool f = true) {
cout << (f ? "Bob" : "Alice") << endl;
return f;
}
// Takahashi Aoki
inline bool Takahashi(bool f = true) {
cout << (f ? "Takahashi" : "Aoki") << endl;
return f;
}
inline bool Aoki(bool f = true) {
cout << (f ? "Aoki" : "Takahashi") << endl;
return f;
}
} // namespace yesno
using namespace yesno;
} // namespace templates
using namespace templates;
template <int MOD>
struct Modint {
int x;
Modint() : x(0) {}
Modint(int64_t y) {
if (y >= 0)
x = y % MOD;
else
x = (y % MOD + MOD) % MOD;
}
Modint &operator+=(const Modint &p) {
x += p.x;
if (x >= MOD) x -= MOD;
return *this;
}
Modint &operator-=(const Modint &p) {
x -= p.x;
if (x < 0) x += MOD;
return *this;
}
Modint &operator*=(const Modint &p) {
x = int(1LL * x * p.x % MOD);
return *this;
}
Modint &operator/=(const Modint &p) {
*this *= p.inverse();
return *this;
}
Modint &operator%=(const Modint &p) {
assert(p.x == 0);
return *this;
}
Modint operator-() const {
return Modint(-x);
}
Modint &operator++() {
x++;
if (x == MOD) x = 0;
return *this;
}
Modint &operator--() {
if (x == 0) x = MOD;
x--;
return *this;
}
Modint operator++(int) {
Modint result = *this;
++*this;
return result;
}
Modint operator--(int) {
Modint result = *this;
--*this;
return result;
}
friend Modint operator+(const Modint &lhs, const Modint &rhs) {
return Modint(lhs) += rhs;
}
friend Modint operator-(const Modint &lhs, const Modint &rhs) {
return Modint(lhs) -= rhs;
}
friend Modint operator*(const Modint &lhs, const Modint &rhs) {
return Modint(lhs) *= rhs;
}
friend Modint operator/(const Modint &lhs, const Modint &rhs) {
return Modint(lhs) /= rhs;
}
friend Modint operator%(const Modint &lhs, const Modint &rhs) {
assert(rhs.x == 0);
return Modint(lhs);
}
bool operator==(const Modint &p) const {
return x == p.x;
}
bool operator!=(const Modint &p) const {
return x != p.x;
}
bool operator<(const Modint &rhs) const {
return x < rhs.x;
}
bool operator<=(const Modint &rhs) const {
return x <= rhs.x;
}
bool operator>(const Modint &rhs) const {
return x > rhs.x;
}
bool operator>=(const Modint &rhs) const {
return x >= rhs.x;
}
Modint inverse() const {
int a = x, b = MOD, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
a -= t * b;
u -= t * v;
std::swap(a, b);
std::swap(u, v);
}
return Modint(u);
}
Modint pow(int64_t k) const {
Modint ret(1);
Modint y(x);
while (k > 0) {
if (k & 1) ret *= y;
y *= y;
k >>= 1;
}
return ret;
}
std::pair<int, int> to_frac(int max_n = 1000) const {
int y = x;
for (int i = 1; i <= max_n; i++) {
if (y <= max_n) {
return {y, i};
} else if (MOD - y <= max_n) {
return {-(MOD - y), i};
}
y = (y + x) % MOD;
}
return {-1, -1};
}
friend std::ostream &operator<<(std::ostream &os, const Modint &p) {
return os << p.x;
}
friend std::istream &operator>>(std::istream &is, Modint &p) {
int64_t y;
is >> y;
p = Modint<MOD>(y);
return (is);
}
static int get_mod() {
return MOD;
}
};
struct Arbitrary_Modint {
int x;
static int MOD;
static void set_mod(int mod) {
MOD = mod;
}
Arbitrary_Modint() : x(0) {}
Arbitrary_Modint(int64_t y) {
if (y >= 0)
x = y % MOD;
else
x = (y % MOD + MOD) % MOD;
}
Arbitrary_Modint &operator+=(const Arbitrary_Modint &p) {
x += p.x;
if (x >= MOD) x -= MOD;
return *this;
}
Arbitrary_Modint &operator-=(const Arbitrary_Modint &p) {
x -= p.x;
if (x < 0) x += MOD;
return *this;
}
Arbitrary_Modint &operator*=(const Arbitrary_Modint &p) {
x = int(1LL * x * p.x % MOD);
return *this;
}
Arbitrary_Modint &operator/=(const Arbitrary_Modint &p) {
*this *= p.inverse();
return *this;
}
Arbitrary_Modint &operator%=(const Arbitrary_Modint &p) {
assert(p.x == 0);
return *this;
}
Arbitrary_Modint operator-() const {
return Arbitrary_Modint(-x);
}
Arbitrary_Modint &operator++() {
x++;
if (x == MOD) x = 0;
return *this;
}
Arbitrary_Modint &operator--() {
if (x == 0) x = MOD;
x--;
return *this;
}
Arbitrary_Modint operator++(int) {
Arbitrary_Modint result = *this;
++*this;
return result;
}
Arbitrary_Modint operator--(int) {
Arbitrary_Modint result = *this;
--*this;
return result;
}
friend Arbitrary_Modint operator+(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) += rhs;
}
friend Arbitrary_Modint operator-(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) -= rhs;
}
friend Arbitrary_Modint operator*(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) *= rhs;
}
friend Arbitrary_Modint operator/(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) /= rhs;
}
friend Arbitrary_Modint operator%(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
assert(rhs.x == 0);
return Arbitrary_Modint(lhs);
}
bool operator==(const Arbitrary_Modint &p) const {
return x == p.x;
}
bool operator!=(const Arbitrary_Modint &p) const {
return x != p.x;
}
bool operator<(const Arbitrary_Modint &rhs) {
return x < rhs.x;
}
bool operator<=(const Arbitrary_Modint &rhs) {
return x <= rhs.x;
}
bool operator>(const Arbitrary_Modint &rhs) {
return x > rhs.x;
}
bool operator>=(const Arbitrary_Modint &rhs) {
return x >= rhs.x;
}
Arbitrary_Modint inverse() const {
int a = x, b = MOD, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
a -= t * b;
u -= t * v;
std::swap(a, b);
std::swap(u, v);
}
return Arbitrary_Modint(u);
}
Arbitrary_Modint pow(int64_t k) const {
Arbitrary_Modint ret(1);
Arbitrary_Modint y(x);
while (k > 0) {
if (k & 1) ret *= y;
y *= y;
k >>= 1;
}
return ret;
}
friend std::ostream &operator<<(std::ostream &os, const Arbitrary_Modint &p) {
return os << p.x;
}
friend std::istream &operator>>(std::istream &is, Arbitrary_Modint &p) {
int64_t y;
is >> y;
p = Arbitrary_Modint(y);
return (is);
}
static int get_mod() {
return MOD;
}
};
int Arbitrary_Modint::MOD = 998244353;
using modint9 = Modint<998244353>;
using modint1 = Modint<1000000007>;
using modint = Arbitrary_Modint;
using mint = modint9;
template <typename mint>
struct NumberTheoreticTransform {
static std::vector<mint> roots, iroots, rate3, irate3;
static int max_base;
NumberTheoreticTransform() = default;
static void init() {
if (!roots.empty()) return;
const unsigned mod = mint::get_mod();
auto tmp = mod - 1;
max_base = 0;
while (tmp % 2 == 0) {
tmp >>= 1;
max_base++;
}
mint root = 2;
while (root.pow((mod - 1) >> 1) == 1) root++;
roots.resize(max_base + 1);
iroots.resize(max_base + 1);
rate3.resize(max_base + 1);
irate3.resize(max_base + 1);
roots[max_base] = root.pow((mod - 1) >> max_base);
iroots[max_base] = mint(1) / roots[max_base];
for (int i = max_base - 1; i >= 0; i--) {
roots[i] = roots[i + 1] * roots[i + 1];
iroots[i] = iroots[i + 1] * iroots[i + 1];
}
mint prod = 1, iprod = 1;
for (int i = 0; i <= max_base - 3; i++) {
rate3[i] = roots[i + 3] * prod;
irate3[i] = iroots[i + 3] * iprod;
prod *= iroots[i + 3];
iprod *= roots[i + 3];
}
}
static void ntt(std::vector<mint> &A) {
init();
int n = int(A.size());
int h = __builtin_ctz(n);
int le = 0;
mint imag = roots[2];
if (h & 1) {
int p = 1 << (h - 1);
for (int i = 0; i < p; i++) {
auto r = A[i + p];
A[i + p] = A[i] - r;
A[i] += r;
}
le++;
}
for (; le + 1 < h; le += 2) {
int p = 1 << (h - le - 2);
for (int i = 0; i < p; i++) {
auto a0 = A[i];
auto a1 = A[i + p];
auto a2 = A[i + 2 * p];
auto a3 = A[i + 3 * p];
auto a1na3imag = (a1 - a3) * imag;
A[i] = a0 + a2 + a1 + a3;
A[i + p] = a0 + a2 - (a1 + a3);
A[i + 2 * p] = a0 - a2 + a1na3imag;
A[i + 3 * p] = a0 - a2 - a1na3imag;
}
mint rot = rate3[0];
for (int s = 1; s < (1 << le); s++) {
int offset = s << (h - le);
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
for (int i = 0; i < p; i++) {
auto a0 = A[i + offset];
auto a1 = A[i + offset + p] * rot;
auto a2 = A[i + offset + 2 * p] * rot2;
auto a3 = A[i + offset + 3 * p] * rot3;
auto a1na3imag = (a1 - a3) * imag;
A[i + offset] = a0 + a2 + a1 + a3;
A[i + offset + p] = a0 + a2 - (a1 + a3);
A[i + offset + 2 * p] = a0 - a2 + a1na3imag;
A[i + offset + 3 * p] = a0 - a2 - a1na3imag;
}
rot *= rate3[__builtin_ctz(~s)];
}
}
}
static void intt(std::vector<mint> &A, bool f = true) {
init();
int n = int(A.size());
int h = __builtin_ctz(n);
int le = h;
mint iimag = iroots[2];
for (; le > 1; le -= 2) {
int p = 1 << (h - le);
for (int i = 0; i < p; i++) {
auto a0 = A[i];
auto a1 = A[i + p];
auto a2 = A[i + 2 * p];
auto a3 = A[i + 3 * p];
auto a2na3iimag = (a2 - a3) * iimag;
A[i] = a0 + a1 + a2 + a3;
A[i + p] = a0 - a1 + a2na3iimag;
A[i + 2 * p] = a0 + a1 - (a2 + a3);
A[i + 3 * p] = a0 - a1 - a2na3iimag;
}
mint irot = irate3[0];
for (int s = 1; s < (1 << (le - 2)); s++) {
int offset = s << (h - le + 2);
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
for (int i = 0; i < p; i++) {
auto a0 = A[i + offset];
auto a1 = A[i + offset + p];
auto a2 = A[i + offset + 2 * p];
auto a3 = A[i + offset + 3 * p];
auto a2na3iimag = (a2 - a3) * iimag;
A[i + offset] = a0 + a1 + a2 + a3;
A[i + offset + p] = (a0 - a1 + a2na3iimag) * irot;
A[i + offset + 2 * p] = (a0 + a1 - (a2 + a3)) * irot2;
A[i + offset + 3 * p] = (a0 - a1 - a2na3iimag) * irot3;
}
irot *= irate3[__builtin_ctz(~s)];
}
}
if (le >= 1) {
int p = 1 << (h - 1);
for (int i = 0; i < p; i++) {
auto ajp = A[i] - A[i + p];
A[i] += A[i + p];
A[i + p] = ajp;
}
}
if (f) {
mint inv = mint(1) / n;
for (int i = 0; i < n; i++) {
A[i] *= inv;
}
}
}
static std::vector<mint> multiply(std::vector<mint> A, std::vector<mint> B) {
int need = int(A.size() + B.size()) - 1;
if (std::min(A.size(), B.size()) < 60u) {
std::vector<mint> C(need, 0);
for (size_t i = 0; i < A.size(); i++)
for (size_t j = 0; j < B.size(); j++) {
C[i + j] += A[i] * B[j];
}
return C;
}
int sz = 1;
while (sz < need) sz <<= 1;
A.resize(sz, 0);
B.resize(sz, 0);
ntt(A);
ntt(B);
mint inv = mint(1) / sz;
for (int i = 0; i < sz; i++) A[i] *= B[i] * inv;
intt(A, false);
A.resize(need);
return A;
}
};
template <typename mint>
std::vector<mint> NumberTheoreticTransform<mint>::roots = std::vector<mint>();
template <typename mint>
std::vector<mint> NumberTheoreticTransform<mint>::iroots = std::vector<mint>();
template <typename mint>
std::vector<mint> NumberTheoreticTransform<mint>::rate3 = std::vector<mint>();
template <typename mint>
std::vector<mint> NumberTheoreticTransform<mint>::irate3 = std::vector<mint>();
template <typename mint>
int NumberTheoreticTransform<mint>::max_base = 0;
template <typename T, typename S>
T modpow(T a, S b, T MOD) {
T ret = 1;
while (b > 0) {
if (b & 1) {
ret *= a;
ret %= MOD;
}
a *= a;
a %= MOD;
b >>= 1;
}
return ret;
}
template <typename T>
T cipolla(T a, T MOD) {
if (MOD == 2)
return a;
else if (a == 0)
return 0;
else if (modpow(a, (MOD - 1) / 2, MOD) != 1)
return -1;
T b = 1;
while (modpow((b * b + MOD - a) % MOD, (MOD - 1) / 2, MOD) == 1) {
b++;
}
T base = (b * b + MOD - a) % MOD;
auto multi = [&](T a0, T b0, T a1, T b1) -> std::pair<T, T> {
return {(a0 * a1 + (b0 * b1 % MOD) * base) % MOD, (a0 * b1 + b0 * a1) % MOD};
};
auto pow_ = [&](auto self, T a, T b, T n) -> std::pair<T, T> {
if (n == 0) return {1, 0};
auto tmp = multi(a, b, a, b);
auto ret = self(self, tmp.first, tmp.second, n / 2);
if (n & 1) {
ret = multi(ret.first, ret.second, a, b);
}
return ret;
};
return pow_(pow_, b, 1LL, (MOD + 1) / 2).first;
}
template <typename mint>
struct FormalPowerSeries : std::vector<mint> {
using std::vector<mint>::vector;
using FPS = FormalPowerSeries;
static std::vector<mint> inv_x;
void shrink() {
while (this->size() && this->back() == mint(0)) {
this->pop_back();
}
}
FPS &operator+=(const FPS &A) {
if (A.size() > this->size()) this->resize(A.size());
for (size_t i = 0; i < A.size(); i++) (*this)[i] += A[i];
return *this;
}
FPS &operator+=(const mint &x) {
if (this->empty()) this->resize(1);
(*this)[0] += x;
return *this;
}
FPS &operator-=(const FPS &A) {
if (A.size() > this->size()) this->resize(A.size());
for (size_t i = 0; i < A.size(); i++) (*this)[i] -= A[i];
return *this;
}
FPS &operator-=(const mint &x) {
if (this->empty()) this->resize(1);
(*this)[0] -= x;
return *this;
}
FPS &operator*=(const FPS &A) {
if (this->empty() || A.empty()) {
this->clear();
return *this;
}
auto res = NumberTheoreticTransform<mint>::multiply(*this, A);
return *this = {begin(res), end(res)};
}
FPS &operator*=(const mint &x) {
for (size_t i = 0; i < this->size(); i++) (*this)[i] *= x;
return *this;
}
FPS operator+(const FPS &A) const {
return FPS(*this) += A;
}
FPS operator+(const mint &x) const {
return FPS(*this) += x;
}
FPS operator-(const FPS &A) const {
return FPS(*this) -= A;
}
FPS operator-(const mint &x) const {
return FPS(*this) -= x;
}
FPS operator*(const FPS &A) const {
return FPS(*this) *= A;
}
FPS operator*(const mint &x) const {
return FPS(*this) *= x;
}
FPS operator-() const {
FPS ret(this->size);
for (size_t i = 0; i < this->size(); i++) ret[i] = -(*this)[i];
return ret;
}
FPS inv(int deg = -1) {
assert((*this)[0] != mint(0));
if (deg == -1) deg = this->size();
FPS g = {mint(1) / (*this)[0]};
int l = 1;
while (l < deg) {
FPS tmp = g * 2;
l <<= 1;
FPS tmp2;
g *= g;
if (int(this->size()) >= l)
tmp2 = FPS({this->begin(), this->begin() + l}) * g;
else
tmp2 = (*this) * g;
g = tmp - tmp2;
g.resize(l);
}
g.resize(deg);
return g;
}
void iinv(int deg = -1) {
*this = inv(deg);
}
FPS differential() {
FPS ret(this->size() - 1);
for (size_t i = 0; i < this->size() - 1; i++) ret[i] = (*this)[i + 1] * (i + 1);
return ret;
}
void idifferential() {
*this = this->differential();
}
void extend_inv(int n) {
int bn = inv_x.size();
if (n >= bn) {
inv_x.resize(n + 1, 0);
if (bn == 0) {
inv_x[0] = 0;
inv_x[1] = 1;
bn = 2;
}
long long mod = mint::get_mod();
for (int i = bn; i <= n; i++) {
inv_x[i] = mod - inv_x[mod % i].x * (mod / i) % mod;
}
}
}
FPS integral() {
extend_inv(this->size());
FPS ret(this->size() + 1);
for (size_t i = 0; i < this->size(); i++) ret[i + 1] = (*this)[i] * inv_x[i + 1];
return ret;
}
void iintegral() {
*this = this->integral();
}
FPS log(int deg = -1) {
assert((*this)[0] == mint(1));
if (deg == -1) deg = this->size();
FPS B = (this->differential()) * (this->inv());
B.resize(deg - 1);
return B.integral();
}
void ilog(int deg = -1) {
*this = this->log(deg);
}
FPS exp(int deg = -1) {
assert((*this)[0] == mint(0));
if (deg == -1) deg = this->size();
FPS g = {1};
int l = 1;
while (l < deg * 2) {
l *= 2;
FPS tmp = {1};
tmp -= g.log(l);
if (int(this->size()) >= l)
tmp += FPS({this->begin(), this->begin() + l});
else
tmp += (*this);
g *= tmp;
g.resize(l);
}
g.resize(deg);
return g;
}
void iexp(int deg = -1) {
*this = this->exp(deg);
}
FPS pow(long long k, int deg = -1) {
if (deg == -1) deg = this->size();
if (k == 0) {
FPS ret(deg, 0);
ret[0] = 1;
return ret;
}
int p = -1;
for (int i = 0; i < deg; i++) {
if ((*this)[i] != 0) {
p = i;
break;
}
}
if (p == -1 || p > deg / k) {
FPS ret(deg, 0);
return ret;
}
mint inv = mint(1) / (*this)[p];
FPS A = FPS({(*this).begin() + p, (*this).end()});
A *= inv;
A.ilog(deg);
A *= k % mint::get_mod();
A.iexp(deg);
FPS B(p * k, 0);
B.insert(B.end(), A.begin(), A.begin() + (deg - p * k));
B *= (*this)[p].pow(k);
return B;
}
void ipow(long long k, int deg = -1) {
*this = this->pow(k, deg);
}
FPS sqrt(int deg = -1) {
if (deg == -1) deg = this->size();
if (this->size() == 0u) {
FPS ret(deg, 0);
return ret;
}
if ((*this)[0] == mint(0)) {
for (size_t i = 1; i < this->size(); i++) {
if ((*this)[i] != 0) {
if (i & 1) {
FPS ret;
return ret;
}
if (deg <= int(i / 2)) break;
FPS ret = FPS({this->begin() + i, this->end()}).sqrt(deg - i / 2);
if (ret.size() == 0u) return ret;
FPS ret2(i / 2, 0);
ret2.insert(ret2.end(), ret.begin(), ret.end());
std::swap(ret, ret2);
if (int(ret.size()) < deg) ret.resize(deg);
return ret;
}
}
FPS ret(deg, 0);
return ret;
}
long long sq = cipolla<long long>((*this)[0].x, mint::get_mod());
if (sq == -1) {
FPS ret;
return ret;
}
mint inv2 = mint(1) / 2;
FPS g = {sq};
int l = 1;
while (l < deg) {
l *= 2;
if (int(this->size()) >= l)
g += FPS({this->begin(), this->begin() + l}) * g.inv(l);
else
g += (*this) * g.inv(l);
g *= inv2;
}
g.resize(deg);
return g;
}
void isqrt(int deg = -1) {
*this = this->sqrt(deg);
}
FPS taylorshift(mint a) {
auto A = (*this);
int deg = A.size();
extend_inv(deg);
mint fac = 1;
for (int i = 0; i < deg; i++) {
A[i] *= fac;
fac *= (i + 1);
}
reverse(A.begin(), A.end());
FPS g(deg, 0);
g[0] = 1;
for (int i = 1; i < deg; i++) g[i] = g[i - 1] * a * inv_x[i];
A *= g;
if (int(A.size()) > deg) A.resize(deg);
reverse(A.begin(), A.end());
mint invfac = 1;
for (int i = 0; i < deg; i++) {
A[i] *= invfac;
invfac *= inv_x[i + 1];
}
return A;
}
void itaylorshift(mint a) {
int deg = this->size();
extend_inv(deg);
mint fac = 1;
for (int i = 0; i < deg; i++) {
(*this)[i] *= fac;
fac *= (i + 1);
}
reverse(this->begin(), this->end());
FPS g(deg, 0);
g[0] = 1;
for (int i = 1; i < deg; i++) g[i] = g[i - 1] * a * inv_x[i];
(*this) *= g;
if (int(this->size()) > deg) this->resize(deg);
reverse(this->begin(), this->end());
mint invfac = 1;
for (int i = 0; i < deg; i++) {
(*this)[i] *= invfac;
invfac *= inv_x[i + 1];
}
}
std::pair<FPS, FPS> division_of_polynomial(FPS G) {
FPS F = *this;
if (F.size() < G.size()) {
return {{}, F};
}
reverse(F.begin(), F.end());
reverse(G.begin(), G.end());
int deg = F.size() - G.size() + 1u;
auto Q = F * G.inv(deg);
if (int(Q.size()) > deg) Q.resize(deg);
reverse(Q.begin(), Q.end());
reverse(F.begin(), F.end());
reverse(G.begin(), G.end());
auto R = F - G * Q;
R.shrink();
return {Q, R};
}
std::vector<mint> multipoint_evaluation(std::vector<mint> &X) {
int m = X.size();
int m2 = 1;
while (m2 <= m - 1) m2 *= 2;
std::vector<FPS> G(m2 << 1, FPS(1, 1));
for (int i = 0; i < m; i++) G[m2 + i] = {-X[i], 1};
for (int i = m2 - 1; i >= 0; i--) G[i] = G[i << 1] * G[(i << 1) | 1];
G[1] = this->division_of_polynomial(G[1]).second;
for (int i = 2; i < m2 + m; i++) G[i] = G[i >> 1].division_of_polynomial(G[i]).second;
std::vector<mint> Y(m);
for (int i = 0; i < m; i++) {
if (G[m2 + i].empty())
Y[i] = 0;
else
Y[i] = G[m2 + i][0];
}
return Y;
}
std::vector<long long> multipoint_evaluation(std::vector<long long> &X) {
int m = X.size();
int m2 = 1;
while (m2 <= m - 1) m2 *= 2;
std::vector<FPS> G(m2 << 1, FPS(1, 1));
for (int i = 0; i < m; i++) G[m2 + i] = {-X[i], 1};
for (int i = m2 - 1; i >= 0; i--) G[i] = G[i << 1] * G[(i << 1) | 1];
G[1] = this->division_of_polynomial(G[1]).second;
for (int i = 2; i < m2 + m; i++) G[i] = G[i >> 1].division_of_polynomial(G[i]).second;
std::vector<long long> Y(m);
for (int i = 0; i < m; i++) {
if (G[m2 + i].empty())
Y[i] = 0;
else
Y[i] = G[m2 + i][0].x;
}
return Y;
}
friend std::ostream &operator<<(std::ostream &os, const FPS &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << ' ';
}
return os;
}
friend std::istream &operator>>(std::istream &is, FPS &A) {
for (size_t i = 0; i < A.size(); i++) {
is >> A[i];
}
return (is);
}
};
template <typename mint>
std::vector<mint> FormalPowerSeries<mint>::inv_x = std::vector<mint>();
using FPS = FormalPowerSeries<mint>;
void solve() {
LL(n);
VEC(mint, A, n);
vec(FPS, F, n);
fori(i, n) F[i] = {1, A[i]};
for (ll i = 0; (1 << i) < n; i++) {
fori(j, n) {
if ((j >> i) & 1) F[j - (1 << i)] *= F[j];
}
}
mint ans = 0;
fori(i, 1, n + 1) {
ans += F[0][i] * mint(i).pow(n - i);
}
print(ans);
}
int main() {
#ifndef INTERACTIVE
std::cin.tie(0)->sync_with_stdio(0);
#endif
// std::cout << std::fixed << std::setprecision(12);
int t;
t = 1;
// std::cin >> t;
while (t--) solve();
return 0;
}
// // #pragma GCC target("avx2")
// // #pragma GCC optimize("O3")
// // #pragma GCC optimize("unroll-loops")
// // #define INTERACTIVE
//
// #include "kyopro-cpp/template.hpp"
//
// #include "misc/Modint.hpp"
// using mint = modint9;
// #include "polynomial/FormalPowerSeries.hpp"
// using FPS = FormalPowerSeries<mint>;
//
// void solve() {
// LL(n);
// VEC(mint, A, n);
// vec(FPS, F, n);
// fori(i, n) F[i] = {1, A[i]};
// for (ll i = 0; (1 << i) < n; i++) {
// fori(j, n) {
// if ((j >> i) & 1) F[j - (1 << i)] *= F[j];
// }
// }
//
// mint ans = 0;
// fori(i, 1, n + 1) {
// ans += F[0][i] * mint(i).pow(n - i);
// }
// print(ans);
// }
//
// int main() {
// #ifndef INTERACTIVE
// std::cin.tie(0)->sync_with_stdio(0);
// #endif
// // std::cout << std::fixed << std::setprecision(12);
// int t;
// t = 1;
// // std::cin >> t;
// while (t--) solve();
// return 0;
// }