This documentation is automatically generated by online-judge-tools/verification-helper
#include <iostream>
#include <vector>
using namespace std;
using ll = long long;
// ----- Mint -----
ll MOD{998244353LL}; // This is dummy. This is needed for global declearation.
constexpr ll MAX_SIZE{300010LL};
/*
Slow manipulations:
- Mint power(ll N) const
- Mint &operator/=(Mint const &a)
- Mint operator/(Mint const &a)
Instead of using these, consider using for-loop and base
e.g.
mint base{1};
for (auto j = MOD - 1; j >= 0; j--)
{
ans[j] -= base * C(MOD - 1, j);
base *= -i;
}
*/
class Mint
{
public:
ll x;
Mint() : x{0LL} {}
Mint(ll x) : x{(x % MOD + MOD) % MOD} {}
Mint operator-() const { return x ? MOD - x : 0; }
Mint &operator+=(Mint const &a)
{
if ((x += a.x) >= MOD)
{
x -= MOD;
}
return *this;
}
Mint &operator-=(Mint const &a) { return *this += -a; }
Mint &operator++() { return *this += 1; }
Mint operator++(int)
{
Mint tmp{*this};
++*this;
return tmp;
}
Mint &operator--() { return *this -= 1; }
Mint operator--(int)
{
Mint tmp{*this};
--*this;
return tmp;
}
Mint &operator*=(Mint const &a)
{
(x *= a.x) %= MOD;
return *this;
}
Mint &operator/=(Mint const &a)
{
Mint b{a};
return *this *= b.power(MOD - 2);
}
Mint operator+(Mint const &a) const { return Mint(*this) += a; }
Mint operator-(Mint const &a) const { return Mint(*this) -= a; }
Mint operator*(Mint const &a) const { return Mint(*this) *= a; }
Mint operator/(Mint const &a) const { return Mint(*this) /= a; }
bool operator<(Mint const &a) const { return x < a.x; }
bool operator<=(Mint const &a) const { return x <= a.x; }
bool operator>(Mint const &a) const { return x > a.x; }
bool operator>=(Mint const &a) const { return x >= a.x; }
bool operator==(Mint const &a) const { return x == a.x; }
bool operator!=(Mint const &a) const { return !(*this == a); }
Mint power(ll N) const
{
if (N == 0)
{
return 1;
}
else if (N % 2 == 1)
{
return *this * power(N - 1);
}
else
{
Mint half = power(N / 2);
return half * half;
}
}
};
Mint operator+(ll lhs, Mint const &rhs)
{
return rhs + lhs;
}
Mint operator-(ll lhs, Mint const &rhs)
{
return -rhs + lhs;
}
Mint operator*(ll lhs, Mint const &rhs)
{
return rhs * lhs;
}
Mint operator/(ll lhs, Mint const &rhs)
{
return Mint{lhs} / rhs;
}
istream &operator>>(istream &stream, Mint &a)
{
return stream >> a.x;
}
ostream &operator<<(ostream &stream, Mint const &a)
{
return stream << a.x;
}
// ----- Combination -----
class Combination
{
public:
vector<Mint> inv, fact, factinv;
Combination() : inv(MAX_SIZE), fact(MAX_SIZE), factinv(MAX_SIZE)
{
inv[1] = 1;
for (auto i = 2LL; i < MAX_SIZE; i++)
{
inv[i] = (-inv[MOD % i]) * (MOD / i);
}
fact[0] = factinv[0] = 1;
for (auto i = 1LL; i < MAX_SIZE; i++)
{
fact[i] = Mint(i) * fact[i - 1];
factinv[i] = inv[i] * factinv[i - 1];
}
}
Mint operator()(int n, int k)
{
if (n >= 0 && k >= 0 && n - k >= 0)
{
return fact[n] * factinv[k] * factinv[n - k];
}
return 0;
}
Mint catalan(int x, int y)
{
return (*this)(x + y, y) - (*this)(x + y, y - 1);
}
};
#line 1 "Tools/Mint_MOD.cpp"
#include <iostream>
#include <vector>
using namespace std;
using ll = long long;
// ----- Mint -----
ll MOD{998244353LL}; // This is dummy. This is needed for global declearation.
constexpr ll MAX_SIZE{300010LL};
/*
Slow manipulations:
- Mint power(ll N) const
- Mint &operator/=(Mint const &a)
- Mint operator/(Mint const &a)
Instead of using these, consider using for-loop and base
e.g.
mint base{1};
for (auto j = MOD - 1; j >= 0; j--)
{
ans[j] -= base * C(MOD - 1, j);
base *= -i;
}
*/
class Mint
{
public:
ll x;
Mint() : x{0LL} {}
Mint(ll x) : x{(x % MOD + MOD) % MOD} {}
Mint operator-() const { return x ? MOD - x : 0; }
Mint &operator+=(Mint const &a)
{
if ((x += a.x) >= MOD)
{
x -= MOD;
}
return *this;
}
Mint &operator-=(Mint const &a) { return *this += -a; }
Mint &operator++() { return *this += 1; }
Mint operator++(int)
{
Mint tmp{*this};
++*this;
return tmp;
}
Mint &operator--() { return *this -= 1; }
Mint operator--(int)
{
Mint tmp{*this};
--*this;
return tmp;
}
Mint &operator*=(Mint const &a)
{
(x *= a.x) %= MOD;
return *this;
}
Mint &operator/=(Mint const &a)
{
Mint b{a};
return *this *= b.power(MOD - 2);
}
Mint operator+(Mint const &a) const { return Mint(*this) += a; }
Mint operator-(Mint const &a) const { return Mint(*this) -= a; }
Mint operator*(Mint const &a) const { return Mint(*this) *= a; }
Mint operator/(Mint const &a) const { return Mint(*this) /= a; }
bool operator<(Mint const &a) const { return x < a.x; }
bool operator<=(Mint const &a) const { return x <= a.x; }
bool operator>(Mint const &a) const { return x > a.x; }
bool operator>=(Mint const &a) const { return x >= a.x; }
bool operator==(Mint const &a) const { return x == a.x; }
bool operator!=(Mint const &a) const { return !(*this == a); }
Mint power(ll N) const
{
if (N == 0)
{
return 1;
}
else if (N % 2 == 1)
{
return *this * power(N - 1);
}
else
{
Mint half = power(N / 2);
return half * half;
}
}
};
Mint operator+(ll lhs, Mint const &rhs)
{
return rhs + lhs;
}
Mint operator-(ll lhs, Mint const &rhs)
{
return -rhs + lhs;
}
Mint operator*(ll lhs, Mint const &rhs)
{
return rhs * lhs;
}
Mint operator/(ll lhs, Mint const &rhs)
{
return Mint{lhs} / rhs;
}
istream &operator>>(istream &stream, Mint &a)
{
return stream >> a.x;
}
ostream &operator<<(ostream &stream, Mint const &a)
{
return stream << a.x;
}
// ----- Combination -----
class Combination
{
public:
vector<Mint> inv, fact, factinv;
Combination() : inv(MAX_SIZE), fact(MAX_SIZE), factinv(MAX_SIZE)
{
inv[1] = 1;
for (auto i = 2LL; i < MAX_SIZE; i++)
{
inv[i] = (-inv[MOD % i]) * (MOD / i);
}
fact[0] = factinv[0] = 1;
for (auto i = 1LL; i < MAX_SIZE; i++)
{
fact[i] = Mint(i) * fact[i - 1];
factinv[i] = inv[i] * factinv[i - 1];
}
}
Mint operator()(int n, int k)
{
if (n >= 0 && k >= 0 && n - k >= 0)
{
return fact[n] * factinv[k] * factinv[n - k];
}
return 0;
}
Mint catalan(int x, int y)
{
return (*this)(x + y, y) - (*this)(x + y, y - 1);
}
};