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P1313 [NOIP2011 提高组] 计算系数

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https://www.luogu.com.cn/record/80041822
This commit is contained in:
Baoshuo Ren 2022-07-18 10:13:33 +08:00
parent 3a9f733349
commit 6fcc52aaf7
Signed by: baoshuo
GPG Key ID: 00CB9680AB29F51A
1 changed files with 52 additions and 15 deletions
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67
Luogu/P1313/P1313.cpp
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@ -1,4 +1,6 @@
#include <iostream>
#include <array>
#include <type_traits>
using std::cin;
using std::cout;
@ -7,8 +9,57 @@ const char endl = '\n';
const int N = 1005;
const int mod = 1e4 + 7;
template <int x>
using number = std::integral_constant<int, x>;
template <int n>
struct factorial : number<static_cast<long long>(n) * factorial<n - 1>::value % mod> {};
template <>
struct factorial<0> : number<1> {};
template <int... S>
constexpr std::array<int, sizeof...(S)> get_factorial_table_impl(std::integer_sequence<int, S...>) {
return {factorial<S>::value...};
}
template <int S>
constexpr auto get_factorial_table() {
return get_factorial_table_impl(std::make_integer_sequence<int, S>{});
}
template <int n>
struct inverse : number<static_cast<long long>(mod - (mod / n)) * inverse<mod % n>::value % mod> {};
template <>
struct inverse<1> : number<1> {};
template <>
struct inverse<0> : number<1> {};
template <int n>
struct factorial_inverse : number<static_cast<long long>(factorial_inverse<n - 1>::value) * inverse<n>::value % mod> {};
template <>
struct factorial_inverse<1> : number<1> {};
template <>
struct factorial_inverse<0> : number<1> {};
template <int... S>
constexpr std::array<int, sizeof...(S)> get_factorial_inverse_table_impl(std::integer_sequence<int, S...>) {
return {factorial_inverse<S>::value...};
}
template <int S>
constexpr auto get_factorial_inverse_table() {
return get_factorial_inverse_table_impl(std::make_integer_sequence<int, S>{});
}
int a, b, k, n, m;
int fac[N], inv[N];
constexpr auto fac = get_factorial_table<N>(),
inv = get_factorial_inverse_table<N>();
int binpow(int a, int b) {
int res = 1;
@ -29,20 +80,6 @@ int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
fac[0] = 1;
for (int i = 1; i <= 1000; i++) {
fac[i] = 1ll * fac[i - 1] * i % mod;
}
inv[0] = inv[1] = 1;
for (int i = 2; i <= 1000; i++) {
inv[i] = static_cast<long long>(mod - (mod / i)) * inv[mod % i] % mod;
}
for (int i = 2; i <= 1000; i++) {
inv[i] = static_cast<long long>(inv[i - 1]) * inv[i] % mod;
}
cin >> a >> b >> k >> n >> m;
cout << static_cast<long long>(C(k, n)) * binpow(a, n) % mod * binpow(b, m) % mod << endl;