#include <bits/stdc++.h>
using namespace std;
template <typename T>
T inverse(T a, T m) {
T u = 0, v = 1;
while (a != 0) {
T t = m / a;
m -= t * a; swap(a, m);
u -= t * v; swap(u, v);
}
assert(m == 1);
return u;
}
template <typename T>
class Modular {
public:
using Type = typename decay<decltype(T::value)>::type;
constexpr Modular() : value() {}
template <typename U>
Modular(const U& x) {
value = normalize(x);
}
template <typename U>
static Type normalize(const U& x) {
Type v;
if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
else v = static_cast<Type>(x % mod());
if (v < 0) v += mod();
return v;
}
const Type& operator()() const { return value; }
template <typename U>
explicit operator U() const { return static_cast<U>(value); }
constexpr static Type mod() { return T::value; }
Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
Modular& operator++() { return *this += 1; }
Modular& operator--() { return *this -= 1; }
Modular operator++(int) { Modular result(*this); *this += 1; return result; }
Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
Modular operator-() const { return Modular(-value); }
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
asm(
"divl %4; \n\t"
: "=a" (d), "=d" (m)
: "d" (xh), "a" (xl), "r" (mod())
);
value = m;
#else
value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
return *this;
}
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type& operator*=(const Modular& rhs) {
int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
value = normalize(value * rhs.value - q * mod());
return *this;
}
template <typename U = T>
typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
value = normalize(value * rhs.value);
return *this;
}
Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
template <typename U>
friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename U>
friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename U>
friend std::istream& operator>>(std::istream& stream, Modular<U>& number);
private:
Type value;
};
template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }
template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }
template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
assert(b >= 0);
Modular<T> x = a, res = 1;
U p = b;
while (p > 0) {
if (p & 1) res *= x;
x *= x;
p >>= 1;
}
return res;
}
template <typename T>
string to_string(const Modular<T>& number) {
return to_string(number());
}
template <typename T>
std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
return stream << number();
}
template <typename T>
std::istream& operator>>(std::istream& stream, Modular<T>& number) {
typename common_type<typename Modular<T>::Type, int64_t>::type x;
stream >> x;
number.value = Modular<T>::normalize(x);
return stream;
}
/*
using ModType = int;
struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/
constexpr int md = 1e9 + 7;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int h, w;
cin >> h >> w;
vector<vector<bool>> was(h + 1, vector<bool>(w + 1, false));
vector<vector<Mint>> dp(h + 1, vector<Mint>(w + 1));
function<Mint(int, int)> Solve = [&](int n, int m) {
if (n <= 0 || m <= 0) return (Mint) 1;
if (was[n][m]) return dp[n][m];
was[n][m] = true;
dp[n][m] += (Mint) ((long long) m * (m - 1) / 2) * Solve(n - 1, m - 2);
dp[n][m] += 4 * m * Solve(n - 1, m - 1);
dp[n][m] += Solve(n - 1, m);
dp[n][m] += (Mint) ((long long) (n - 1) * m) * Solve(n - 2, m - 1);
return dp[n][m];
};
cout << Solve(h, w) - 1 << '\n';
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
Output is correct |
| 2 |
Correct |
1 ms |
212 KB |
Output is correct |
| 3 |
Correct |
1 ms |
212 KB |
Output is correct |
| 4 |
Correct |
1 ms |
320 KB |
Output is correct |
| 5 |
Correct |
1 ms |
340 KB |
Output is correct |
| 6 |
Correct |
2 ms |
452 KB |
Output is correct |
| 7 |
Correct |
1 ms |
340 KB |
Output is correct |
| 8 |
Correct |
1 ms |
340 KB |
Output is correct |
| 9 |
Correct |
1 ms |
340 KB |
Output is correct |
| 10 |
Correct |
3 ms |
468 KB |
Output is correct |
| 11 |
Correct |
0 ms |
212 KB |
Output is correct |
| 12 |
Correct |
5 ms |
744 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
Output is correct |
| 2 |
Correct |
1 ms |
212 KB |
Output is correct |
| 3 |
Correct |
1 ms |
212 KB |
Output is correct |
| 4 |
Correct |
1 ms |
320 KB |
Output is correct |
| 5 |
Correct |
1 ms |
340 KB |
Output is correct |
| 6 |
Correct |
2 ms |
452 KB |
Output is correct |
| 7 |
Correct |
1 ms |
340 KB |
Output is correct |
| 8 |
Correct |
1 ms |
340 KB |
Output is correct |
| 9 |
Correct |
1 ms |
340 KB |
Output is correct |
| 10 |
Correct |
3 ms |
468 KB |
Output is correct |
| 11 |
Correct |
0 ms |
212 KB |
Output is correct |
| 12 |
Correct |
5 ms |
744 KB |
Output is correct |
| 13 |
Correct |
1 ms |
340 KB |
Output is correct |
| 14 |
Correct |
1 ms |
852 KB |
Output is correct |
| 15 |
Correct |
333 ms |
23512 KB |
Output is correct |
| 16 |
Correct |
5 ms |
1748 KB |
Output is correct |
| 17 |
Correct |
30 ms |
5460 KB |
Output is correct |
| 18 |
Correct |
68 ms |
6740 KB |
Output is correct |
| 19 |
Correct |
453 ms |
27236 KB |
Output is correct |
| 20 |
Correct |
344 ms |
21844 KB |
Output is correct |
| 21 |
Correct |
166 ms |
14512 KB |
Output is correct |
| 22 |
Correct |
190 ms |
14420 KB |
Output is correct |
| 23 |
Correct |
125 ms |
8532 KB |
Output is correct |
| 24 |
Correct |
616 ms |
37284 KB |
Output is correct |
| 25 |
Correct |
412 ms |
27816 KB |
Output is correct |
| 26 |
Correct |
516 ms |
31832 KB |
Output is correct |
| 27 |
Correct |
574 ms |
35884 KB |
Output is correct |
