結果
| 問題 | No.2503 Typical Path Counting Problem on a Grid |
| ユーザー |
👑  rin204
|
| 提出日時 | 2023-10-13 22:21:22 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 574 ms / 2,000 ms |
| コード長 | 23,430 bytes |
| コンパイル時間 | 3,627 ms |
| コンパイル使用メモリ | 260,884 KB |
| 実行使用メモリ | 42,264 KB |
| 最終ジャッジ日時 | 2023-10-13 22:21:30 |
| 合計ジャッジ時間 | 7,477 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge12 |
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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 | 82 ms
42,172 KB |
| testcase_01 | AC | 129 ms
42,264 KB |
| testcase_02 | AC | 90 ms
42,220 KB |
| testcase_03 | AC | 248 ms
42,260 KB |
| testcase_04 | AC | 397 ms
42,168 KB |
| testcase_05 | AC | 205 ms
42,164 KB |
| testcase_06 | AC | 521 ms
42,172 KB |
| testcase_07 | AC | 574 ms
42,172 KB |
| testcase_08 | AC | 249 ms
42,136 KB |
| testcase_09 | AC | 404 ms
42,056 KB |
ソースコード
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
namespace templates {
// type
using ll = long long;
using ull = unsigned long long;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
#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__)));
// 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
#ifndef RIN__LOCAL
#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 {
// 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>
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;
}
// set<T>
template <typename T>
ostream &operator<<(ostream &os, set<T> &A) {
for (auto itr = A.begin(); itr != A.end(); itr++) {
os << *itr;
if (next(itr) != A.end()) os << ' ';
}
return os;
}
// unordered_set<T>
template <typename T>
ostream &operator<<(ostream &os, unordered_set<T> &A) {
for (auto itr = A.begin(); itr != A.end(); itr++) {
os << *itr;
if (next(itr) != A.end()) os << ' ';
}
return os;
}
// multiset<T>
template <typename T>
ostream &operator<<(ostream &os, multiset<T> &A) {
for (auto itr = A.begin(); itr != A.end(); itr++) {
os << *itr;
if (next(itr) != A.end()) os << ' ';
}
return os;
}
// unordered_multiset<T>
template <typename T>
ostream &operator<<(ostream &os, unordered_multiset<T> &A) {
for (auto itr = A.begin(); itr != A.end(); itr++) {
os << *itr;
if (next(itr) != A.end()) os << endl;
}
return os;
}
// map<S, T>
template <typename S, typename T>
ostream &operator<<(ostream &os, map<S, T> &A) {
for (auto itr = A.begin(); itr != A.end(); itr++) {
os << *itr;
if (next(itr) != A.end()) os << endl;
}
return os;
}
// unordered_map<S, T>
template <typename S, typename T>
ostream &operator<<(ostream &os, unordered_map<S, T> &A) {
for (auto itr = A.begin(); itr != A.end(); itr++) {
os << *itr;
if (next(itr) != A.end()) 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;
}
// queue<T>
template <typename T>
ostream &operator<<(ostream &os, queue<T> &A) {
auto B = A;
while (!B.empty()) {
os << B.front();
B.pop();
if (!B.empty()) os << ' ';
}
return os;
}
// deque<T>
template <typename T>
ostream &operator<<(ostream &os, deque<T> &A) {
auto B = A;
while (!B.empty()) {
os << B.front();
B.pop_front();
if (!B.empty()) os << ' ';
}
return os;
}
// stack<T>
template <typename T>
ostream &operator<<(ostream &os, stack<T> &A) {
auto B = A;
stack<T> C;
while (!B.empty()) {
C.push(B.top());
B.pop();
}
while (!C.empty()) {
os << C.top();
C.pop();
if (!C.empty()) os << ' ';
}
return os;
}
// priority_queue<T>
template <typename T>
ostream &operator<<(ostream &os, priority_queue<T> &A) {
auto B = A;
while (!B.empty()) {
os << B.top();
B.pop();
if (!B.empty()) os << endl;
}
return os;
}
// bitset<N>
template <size_t N>
ostream &operator<<(ostream &os, bitset<N> &A) {
for (size_t i = 0; i < N; i++) {
os << A[i];
}
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(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;
swap(a, b);
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;
}
friend ostream &operator<<(ostream &os, const Modint &p) {
return os << p.x;
}
friend istream &operator>>(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;
swap(a, b);
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 ostream &operator<<(ostream &os, const Arbitrary_Modint &p) {
return os << p.x;
}
friend istream &operator>>(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 type>
struct Matrix {
int n, m;
vector<vector<type>> A;
Matrix() = default;
Matrix(int n, int m) : A(n, vector<type>(m, 0)), n(n), m(m) {}
Matrix(int n) : A(n, vector<type>(n, 0)), n(n), m(n) {}
Matrix(vector<vector<type>> A) : A(A), n(A.size()), m(A[0].size()) {}
inline const vector<type> &operator[](int k) const {
return (A.at(k));
}
inline vector<type> &operator[](int k) {
return (A.at(k));
}
Matrix T() {
Matrix<type> B(m, n);
for (int i = 0; i < m; i++)
for (int j = 0; j < n; j++) {
B.A[i][j] = A[j][i];
}
return B;
}
Matrix &operator+=(const Matrix &B) {
assert(n == B.A.size());
assert(m == B.A[0].size());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) {
this->A[i][j] += B[i][j];
}
return *this;
}
Matrix &operator-=(const Matrix &B) {
assert(n == B.A.size());
assert(m == B.A[0].size());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) {
this->A[i][j] -= B[i][j];
}
return *this;
}
Matrix &operator*=(const Matrix &B) {
int k = B[0].size();
assert(m == B.A.size());
vector<vector<type>> C(n, vector<type>(k, 0));
for (int i = 0; i < n; i++)
for (int j = 0; j < k; j++) {
for (int l = 0; l < m; l++) {
C[i][j] += this->A[i][l] * B[l][j];
}
}
swap(this->A, C);
return *this;
}
Matrix operator+(const Matrix &B) const {
return (Matrix(*this) += B);
}
Matrix operator-(const Matrix &B) const {
return (Matrix(*this) -= B);
}
Matrix operator*(const Matrix &B) const {
return (Matrix(*this) *= B);
}
type det() {
auto arr = A;
assert(n == m);
type ret = 1;
for (int i = 0; i < n; i++) {
if (arr[i][i] == 0) {
bool ng = true;
for (int j = i + 1; j < n; j++) {
if (arr[j][i] == 0) continue;
swap(arr[i], arr[j]);
ret *= -1;
ng = false;
break;
}
if (ng) return 0;
}
ret *= arr[i][i];
type inv = type(1) / arr[i][i];
for (int j = i; j < n; j++) arr[i][j] *= inv;
for (int j = i + 1; j < n; j++) {
type x = arr[j][i];
for (int k = i; k < n; k++) {
arr[j][k] -= arr[i][k] * x;
}
}
}
return ret;
}
void I() {
assert(n == m);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
if (i == j)
A[i][j] = 1;
else
A[i][j] = 0;
}
}
}
Matrix<type> inv() {
assert(n == m);
Matrix<type> ret(n);
ret.I();
auto &B = ret.A;
auto arr = A;
for (int j = 0; j < n; j++) {
int ii = -1;
for (int i = j; i < n; i++) {
if (arr[i][j] != 0) {
ii = i;
break;
}
}
if (ii == -1) {
return {};
}
swap(arr[j], arr[ii]);
swap(B[j], B[ii]);
ii = j;
type inv = type(1) / arr[ii][j];
for (int jj = 0; jj < n; jj++) {
B[ii][jj] *= inv;
arr[ii][jj] *= inv;
}
for (int i = 0; i < n; i++) {
if (i == ii) continue;
type t = arr[i][j];
for (int jj = 0; jj < n; jj++) {
arr[i][jj] -= arr[ii][jj] * t;
B[i][jj] -= B[ii][jj] * t;
}
}
}
return ret;
}
};
template <typename T>
void inp(Matrix<T> &M) {
for (auto &row : M.A) inp(row);
}
template <typename T>
void print(Matrix<T> &M) {
for (auto &row : M.A) print(row);
}
template <typename T>
Matrix<T> Matrix_exp(Matrix<T> A, Matrix<T> B, long long k) {
assert(A.A.size() == A[0].size());
assert(A.A.size() == B.A.size());
assert(B.A[0].size() == 1);
int n = A[0].size();
while (k > 0) {
if (k & 1) B = A * B;
A *= A;
k >>= 1;
}
return B;
}
void solve() {
const ll N = 10000000;
vec(mint, dp, N + 1, 0);
dp[0] = 1;
dp[1] = 2;
fori(i, 2, N + 1) dp[i] = 2 * i * dp[i - 1] + (i - 1) * dp[i - 2];
INT(Q);
fori(Q) {
LL(n, m);
if (n > m) swap(n, m);
if (n == 0) {
print(1);
continue;
} else if (n == m) {
mint ans = dp[n] * dp[n];
ans += dp[n - 1] * dp[n - 1] * n;
print(ans);
continue;
}
Matrix<mint> A(2, 2);
Matrix<mint> B(2, 1);
A[0][0] = 2 * n + 1;
A[0][1] = n;
A[1][0] = 1;
A[1][1] = 0;
B[0][0] = dp[n];
B[1][0] = dp[n - 1];
auto C = Matrix_exp(A, B, m - n);
mint ans = C[0][0] * dp[n];
ans += C[1][0] * n * dp[n - 1];
print(ans);
}
}
int main() {
cin.tie(0)->sync_with_stdio(0);
// cout << fixed << setprecision(12);
int t;
t = 1;
// cin >> t;
while (t--) solve();
return 0;
}