結果
| 問題 | No.3055 Simple Chicken Game |
| ユーザー |
👑  rin204
|
| 提出日時 | 2025-02-02 18:05:08 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,986 ms / 2,000 ms |
| コード長 | 27,762 bytes |
| コンパイル時間 | 4,751 ms |
| コンパイル使用メモリ | 312,252 KB |
| 実行使用メモリ | 496,128 KB |
| 最終ジャッジ日時 | 2025-02-05 00:30:43 |
| 合計ジャッジ時間 | 17,297 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 30 |
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::istream &operator>>(std::istream &is, __int128_t &value) {
std::string str;
is >> str;
value = 0;
int sign = 1;
for (size_t i = 0; i < str.size(); i++) {
if (i == 0 && str[i] == '-') {
sign = -1;
continue;
}
value = value * 10 + str[i] - '0';
}
value *= sign;
return is;
}
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;
}
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 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 = modint;
void solve() {
INT(n, P);
mint::set_mod(P);
using Pd = pair<double, double>;
using Pm = pair<mint, mint>;
vvec(Pm, dp2, n + 1, 2 * n + 3, {0, 0});
vvec(int, to, n + 1, 2 * n + 3, 0);
int zero = n + 1;
{
vvec(Pd, dp, n + 1, 2 * n + 3, {0, 0});
fori(i, n - 1, -1, -1) {
fori(j, -i, i + 1) {
auto score1 = dp[i + 1][zero + j + 1].first * 2 + j / 2.0;
auto score2 = dp[i + 1][zero + j - 1].first + dp[i + 1][zero + j - 1].second;
if (abs(score1 - score2) < 1e-9) {
dp[i][zero + j].first = (2.0 * dp[i + 1][zero + j + 1].first + dp[i + 1][zero + j - 1].first + dp[i + 1][zero + j].first + 1) / 4.0;
dp[i][zero + j].second = (2.0 * dp[i + 1][zero + j + 1].second + 2 + dp[i + 1][zero + j - 1].second + dp[i + 1][zero + j].second) / 4.0;
dp2[i][zero + j].first = (2 * dp2[i + 1][zero + j + 1].first + dp2[i + 1][zero + j - 1].first + dp2[i + 1][zero + j].first + 1) / 4;
dp2[i][zero + j].second = (2 * dp2[i + 1][zero + j + 1].second + 2 + dp2[i + 1][zero + j - 1].second + dp2[i + 1][zero + j].second) / 4;
to[i][zero + j] = 0;
} else if (score1 < score2) {
dp[i][zero + j] = {dp[i + 1][zero + j + 1].first, dp[i + 1][zero + j + 1].second + 1};
dp2[i][zero + j] = {dp2[i + 1][zero + j + 1].first, dp2[i + 1][zero + j + 1].second + 1};
to[i][zero + j] = 1;
} else {
dp[i][zero + j] = {(dp[i + 1][zero + j - 1].first + dp[i + 1][zero + j].first + 1) / 2.0, (dp[i + 1][zero + j - 1].second + dp[i + 1][zero + j].second) / 2.0};
dp2[i][zero + j] = {(dp2[i + 1][zero + j - 1].first + dp2[i + 1][zero + j].first + 1) / 2, (dp2[i + 1][zero + j - 1].second + dp2[i + 1][zero + j].second) / 2};
to[i][zero + j] = 2;
}
}
}
}
{
fori(i, n - 1, -1, -1) {
fori(j, -i, i + 1) {
if (to[i][zero + j] == 0) {
dp2[i][zero + j].first = (2 * dp2[i + 1][zero + j + 1].first + dp2[i + 1][zero + j - 1].first + dp2[i + 1][zero + j].first + 1) / 4;
dp2[i][zero + j].second = (2 * dp2[i + 1][zero + j + 1].second + 2 + dp2[i + 1][zero + j - 1].second + dp2[i + 1][zero + j].second) / 4;
} else if (to[i][zero + j] == 1) {
dp2[i][zero + j] = {dp2[i + 1][zero + j + 1].first, dp2[i + 1][zero + j + 1].second + 1};
} else {
dp2[i][zero + j] = {(dp2[i + 1][zero + j - 1].first + dp2[i + 1][zero + j].first + 1) / 2, (dp2[i + 1][zero + j - 1].second + dp2[i + 1][zero + j].second) / 2};
}
}
}
}
vec(bool, ok, 2 * n + 3, false);
ok[zero] = true;
vvec(mint, prob, n + 1, 2 * n + 3, 0);
prob[0][zero] = 1;
vec(mint, ans, n, 0);
vec(int, cnt, 3, 0);
vec(mint, cum, n + 1, 0);
fori(i, n) {
if (i > 0) cum[i] += cum[i - 1];
vec(bool, nok, 2 * n + 3, false);
fori(j, -i, i + 1) {
if (!ok[zero + j]) continue;
if (to[i][zero + j] == 0) {
prob[i + 1][zero + j - 1] += prob[i][zero + j] / 4;
prob[i + 1][zero + j] += prob[i][zero + j] / 4;
prob[i + 1][zero + j + 1] += prob[i][zero + j] / 2;
nok[zero + j - 1] = true;
nok[zero + j] = true;
nok[zero + j + 1] = true;
cum[i + 1] += prob[i][zero + j] / 4;
} else if (to[i][zero + j] == 1) {
prob[i + 1][zero + j + 1] += prob[i][zero + j];
nok[zero + j + 1] = true;
} else {
prob[i + 1][zero + j - 1] += prob[i][zero + j] / 2;
prob[i + 1][zero + j] += prob[i][zero + j] / 2;
cum[i + 1] += prob[i][zero + j] / 2;
nok[zero + j - 1] = true;
nok[zero + j] = true;
}
mint tt = 0;
if (to[i][zero + j] != 2) {
tt += cum[i];
tt += mint(i - cum[i] + j) / 2;
tt += dp2[i + 1][zero + j + 1].first;
}
if (to[i][zero + j] != 1) {
tt += cum[i];
tt += mint(i - cum[i]) / 2;
tt += mint(dp2[i + 1][zero + j - 1].first + dp2[i + 1][zero + j - 1].second) / 2;
}
if (to[i][zero + j] == 0) tt /= 2;
ans[i] += tt * prob[i][zero + j];
}
swap(ok, nok);
}
fori(i, n) ans[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 = modint;
//
// void solve() {
// INT(n, P);
// mint::set_mod(P);
// using Pd = pair<double, double>;
// using Pm = pair<mint, mint>;
// vvec(Pm, dp2, n + 1, 2 * n + 3, {0, 0});
// vvec(int, to, n + 1, 2 * n + 3, 0);
// int zero = n + 1;
// {
// vvec(Pd, dp, n + 1, 2 * n + 3, {0, 0});
// fori(i, n - 1, -1, -1) {
// fori(j, -i, i + 1) {
// auto score1 = dp[i + 1][zero + j + 1].first * 2 + j / 2.0;
// auto score2 = dp[i + 1][zero + j - 1].first + dp[i + 1][zero + j - 1].second;
// if (abs(score1 - score2) < 1e-9) {
// dp[i][zero + j].first = (2.0 * dp[i + 1][zero + j + 1].first + dp[i + 1][zero + j - 1].first + dp[i + 1][zero + j].first + 1) / 4.0;
// dp[i][zero + j].second = (2.0 * dp[i + 1][zero + j + 1].second + 2 + dp[i + 1][zero + j - 1].second + dp[i + 1][zero + j].second) / 4.0;
// dp2[i][zero + j].first = (2 * dp2[i + 1][zero + j + 1].first + dp2[i + 1][zero + j - 1].first + dp2[i + 1][zero + j].first + 1) / 4;
// dp2[i][zero + j].second = (2 * dp2[i + 1][zero + j + 1].second + 2 + dp2[i + 1][zero + j - 1].second + dp2[i + 1][zero + j].second) / 4;
// to[i][zero + j] = 0;
// } else if (score1 < score2) {
// dp[i][zero + j] = {dp[i + 1][zero + j + 1].first, dp[i + 1][zero + j + 1].second + 1};
// dp2[i][zero + j] = {dp2[i + 1][zero + j + 1].first, dp2[i + 1][zero + j + 1].second + 1};
// to[i][zero + j] = 1;
// } else {
// dp[i][zero + j] = {(dp[i + 1][zero + j - 1].first + dp[i + 1][zero + j].first + 1) / 2.0, (dp[i + 1][zero + j - 1].second + dp[i + 1][zero + j].second) / 2.0};
// dp2[i][zero + j] = {(dp2[i + 1][zero + j - 1].first + dp2[i + 1][zero + j].first + 1) / 2, (dp2[i + 1][zero + j - 1].second + dp2[i + 1][zero + j].second) / 2};
// to[i][zero + j] = 2;
// }
// }
// }
// }
// {
// fori(i, n - 1, -1, -1) {
// fori(j, -i, i + 1) {
// if (to[i][zero + j] == 0) {
// dp2[i][zero + j].first = (2 * dp2[i + 1][zero + j + 1].first + dp2[i + 1][zero + j - 1].first + dp2[i + 1][zero + j].first + 1) / 4;
// dp2[i][zero + j].second = (2 * dp2[i + 1][zero + j + 1].second + 2 + dp2[i + 1][zero + j - 1].second + dp2[i + 1][zero + j].second) / 4;
// } else if (to[i][zero + j] == 1) {
// dp2[i][zero + j] = {dp2[i + 1][zero + j + 1].first, dp2[i + 1][zero + j + 1].second + 1};
// } else {
// dp2[i][zero + j] = {(dp2[i + 1][zero + j - 1].first + dp2[i + 1][zero + j].first + 1) / 2, (dp2[i + 1][zero + j - 1].second + dp2[i + 1][zero + j].second) / 2};
// }
// }
// }
// }
//
// vec(bool, ok, 2 * n + 3, false);
// ok[zero] = true;
// vvec(mint, prob, n + 1, 2 * n + 3, 0);
// prob[0][zero] = 1;
// vec(mint, ans, n, 0);
// vec(int, cnt, 3, 0);
// vec(mint, cum, n + 1, 0);
// fori(i, n) {
// if (i > 0) cum[i] += cum[i - 1];
// vec(bool, nok, 2 * n + 3, false);
// fori(j, -i, i + 1) {
// if (!ok[zero + j]) continue;
// if (to[i][zero + j] == 0) {
// prob[i + 1][zero + j - 1] += prob[i][zero + j] / 4;
// prob[i + 1][zero + j] += prob[i][zero + j] / 4;
// prob[i + 1][zero + j + 1] += prob[i][zero + j] / 2;
// nok[zero + j - 1] = true;
// nok[zero + j] = true;
// nok[zero + j + 1] = true;
// cum[i + 1] += prob[i][zero + j] / 4;
// } else if (to[i][zero + j] == 1) {
// prob[i + 1][zero + j + 1] += prob[i][zero + j];
// nok[zero + j + 1] = true;
// } else {
// prob[i + 1][zero + j - 1] += prob[i][zero + j] / 2;
// prob[i + 1][zero + j] += prob[i][zero + j] / 2;
// cum[i + 1] += prob[i][zero + j] / 2;
// nok[zero + j - 1] = true;
// nok[zero + j] = true;
// }
//
// mint tt = 0;
// if (to[i][zero + j] != 2) {
// tt += cum[i];
// tt += mint(i - cum[i] + j) / 2;
// tt += dp2[i + 1][zero + j + 1].first;
// }
// if (to[i][zero + j] != 1) {
// tt += cum[i];
// tt += mint(i - cum[i]) / 2;
// tt += mint(dp2[i + 1][zero + j - 1].first + dp2[i + 1][zero + j - 1].second) / 2;
// }
// if (to[i][zero + j] == 0) tt /= 2;
// ans[i] += tt * prob[i][zero + j];
// }
// swap(ok, nok);
// }
//
// fori(i, n) ans[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;
// }