結果
| 問題 | No.823 Many Shifts Easy |
| ユーザー |
 Pachicobue
|
| 提出日時 | 2019-04-26 23:12:56 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 4 ms / 2,000 ms |
| コード長 | 10,438 bytes |
| コンパイル時間 | 2,536 ms |
| コンパイル使用メモリ | 206,432 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-05-04 01:02:23 |
| 合計ジャッジ時間 | 2,874 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
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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 | 2 ms
6,812 KB |
| testcase_01 | AC | 1 ms
6,944 KB |
| testcase_02 | AC | 1 ms
6,944 KB |
| testcase_03 | AC | 4 ms
6,944 KB |
| testcase_04 | AC | 2 ms
6,940 KB |
| testcase_05 | AC | 3 ms
6,940 KB |
| testcase_06 | AC | 4 ms
6,940 KB |
| testcase_07 | AC | 1 ms
6,940 KB |
| testcase_08 | AC | 4 ms
6,940 KB |
| testcase_09 | AC | 2 ms
6,940 KB |
ソースコード
#include <bits/stdc++.h>
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"
#define NDEBUG
#define SHOW(...) static_cast<void>(0)
//!===========================================================!//
//! dP dP dP !//
//! 88 88 88 !//
//! 88aaaaa88a .d8888b. .d8888b. .d888b88 .d8888b. 88d888b. !//
//! 88 88 88ooood8 88' '88 88' '88 88ooood8 88' '88 !//
//! 88 88 88. ... 88. .88 88. .88 88. ... 88 !//
//! dP dP '88888P' '88888P8 '88888P8 '88888P' dP !//
//!===========================================================!//
using ld = long double;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr unsigned int MOD = 1000000007;
template <typename T>
constexpr T INF = std::numeric_limits<T>::max() / 4;
template <typename F>
constexpr F PI = static_cast<F>(3.1415926535897932385);
std::mt19937 mt{std::random_device{}()};
template <typename T>
bool chmin(T& a, const T& b) { return a = std::min(a, b), a == b; }
template <typename T>
bool chmax(T& a, const T& b) { return a = std::max(a, b), a == b; }
template <typename T>
std::vector<T> Vec(const std::size_t n, T v) { return std::vector<T>(n, v); }
template <class... Args>
auto Vec(const std::size_t n, Args... args) { return std::vector<decltype(Vec(args...))>(n, Vec(args...)); }
template <typename T>
constexpr T popCount(const T u)
{
#ifdef __has_builtin
return u == 0 ? T(0) : (T)__builtin_popcountll(u);
#else
unsigned long long v = static_cast<unsigned long long>(u);
return v = (v & 0x5555555555555555ULL) + (v >> 1 & 0x5555555555555555ULL), v = (v & 0x3333333333333333ULL) + (v >> 2 & 0x3333333333333333ULL), v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL, static_cast<T>(v * 0x0101010101010101ULL >> 56 & 0x7f);
#endif
}
template <typename T>
constexpr T log2p1(const T u)
{
#ifdef __has_builtin
return u == 0 ? T(0) : T(64 - __builtin_clzll(u));
#else
unsigned long long v = static_cast<unsigned long long>(u);
return v = static_cast<unsigned long long>(v), v |= (v >> 1), v |= (v >> 2), v |= (v >> 4), v |= (v >> 8), v |= (v >> 16), v |= (v >> 32), popCount(v);
#endif
}
template <typename T>
constexpr T clog(const T v) { return v == 0 ? T(0) : log2p1(v - 1); }
template <typename T>
constexpr T msbp1(const T v) { return log2p1(v); }
template <typename T>
constexpr T lsbp1(const T v)
{
#ifdef __has_builtin
return __builtin_ffsll(v);
#else
return v == 0 ? T(0) : popCount((v & (-v)) - T(1)) + T(1);
#endif
}
template <typename T>
constexpr bool ispow2(const T v) { return popCount(v) == 1; }
template <typename T>
constexpr T ceil2(const T v) { return v == 0 ? T(1) : T(1) << log2p1(v - 1); }
template <typename T>
constexpr T floor2(const T v) { return v == 0 ? T(0) : T(1) << (log2p1(v) - 1); }
//!===============================================================!//
//! 88888888b dP .88888. a88888b. 888888ba !//
//! 88 88 d8' '88 d8' '88 88 '8b !//
//! a88aaaa dP. .dP d8888P 88 88 88 88 !//
//! 88 '8bd8' 88 88 YP88 88 88 88 !//
//! 88 .d88b. 88 Y8. .88 Y8. .88 88 .8P !//
//! 88888888P dP' 'dP dP '88888' Y88888P' 8888888P !//
//!===============================================================!//
template <typename T>
constexpr std::pair<T, T> extgcd(const T a, const T b)
{
if (b == 0) { return std::pair<T, T>{1, 0}; }
const auto p = extgcd(b, a % b);
return {p.second, p.first - p.second * (a / b)};
}
template <typename T>
constexpr T inverse(const T a, const T mod) { return (mod + extgcd((mod + a % mod) % mod, mod).first % mod) % mod; }
//!========================================================!//
//! 8888ba.88ba dP dP dP !//
//! 88 '8b '8b 88 88 88 !//
//! 88 88 88 .d8888b. .d888b88 88 88d888b. d8888P !//
//! 88 88 88 88' '88 88' '88 88 88' '88 88 !//
//! 88 88 88 88. .88 88. .88 88 88 88 88 !//
//! dP dP dP '88888P' '88888P8 dP dP dP dP !//
//!========================================================!//
template <uint mod>
class ModInt
{
private:
uint v;
static uint norm(const uint& x) { return x < mod ? x : x - mod; }
static ModInt make(const uint& x)
{
ModInt m;
return m.v = x, m;
}
static ModInt power(ModInt x, ll n)
{
ModInt ans = 1;
for (; n; n >>= 1, x *= x) {
if (n & 1) { ans *= x; }
}
return ans;
}
static ModInt inv(const ModInt& x) { return ModInt{inverse((ll)x.v, (ll)mod)}; }
public:
ModInt() : v{0} {}
ModInt(const ll val) : v{norm(uint(val % (ll)mod + (ll)mod))} {}
ModInt(const ModInt<mod>& n) : v{n()} {}
explicit operator bool() const { return v != 0; }
ModInt<mod>& operator=(const ModInt<mod>& n) { return v = n(), (*this); }
ModInt<mod>& operator=(const ll val) { return v = norm(uint(val % (ll)mod + (ll)mod)), (*this); }
ModInt<mod> operator+() const { return *this; }
ModInt<mod> operator-() const { return make(norm(mod - v)); }
ModInt<mod> operator+(const ModInt<mod>& val) const { return make(norm(v + val())); }
ModInt<mod> operator-(const ModInt<mod>& val) const { return make(norm(v + mod - val())); }
ModInt<mod> operator*(const ModInt<mod>& val) const { return make((uint)((ll)v * val() % (ll)mod)); }
ModInt<mod> operator/(const ModInt<mod>& val) const { return *this * inv(val()); }
ModInt<mod>& operator+=(const ModInt<mod>& val) { return *this = *this + val; }
ModInt<mod>& operator-=(const ModInt<mod>& val) { return *this = *this - val; }
ModInt<mod>& operator*=(const ModInt<mod>& val) { return *this = *this * val; }
ModInt<mod>& operator/=(const ModInt<mod>& val) { return *this = *this / val; }
ModInt<mod> operator+(const ll val) const { return ModInt{v + val}; }
ModInt<mod> operator-(const ll val) const { return ModInt{v - val}; }
ModInt<mod> operator*(const ll val) const { return ModInt{(ll)v * (val % mod)}; }
ModInt<mod> operator/(const ll val) const { return ModInt{(ll)v * inv(val)}; }
template <typename I>
ModInt<mod> operator^(const I n) const { return power(v, n); }
ModInt<mod>& operator+=(const ll val) { return *this = *this + val; }
ModInt<mod>& operator-=(const ll val) { return *this = *this - val; }
ModInt<mod>& operator*=(const ll val) { return *this = *this * val; }
ModInt<mod>& operator/=(const ll val) { return *this = *this / val; }
template <typename I>
ModInt<mod>& operator^=(const I n) { return (*this) = ((*this) ^ n); }
bool operator==(const ModInt<mod>& val) const { return v == val.v; }
bool operator!=(const ModInt<mod>& val) const { return not(*this == val); }
bool operator==(const ll val) const { return v == norm(uint((ll)mod + val % (ll)mod)); }
bool operator!=(const ll val) const { return not(*this == val); }
uint operator()() const { return v; }
};
template <uint mod>
inline ModInt<mod> operator+(const ll val, const ModInt<mod>& n) { return n + val; }
template <uint mod>
inline ModInt<mod> operator-(const ll val, const ModInt<mod>& n) { return ModInt<mod>{val - (ll)n()}; }
template <uint mod>
inline ModInt<mod> operator*(const ll val, const ModInt<mod>& n) { return n * val; }
template <uint mod>
inline ModInt<mod> operator/(const ll val, const ModInt<mod>& n) { return ModInt<mod>(val) / n; }
template <uint mod>
inline bool operator==(const ll val, const ModInt<mod>& n) { return n == val; }
template <uint mod>
inline bool operator!=(const ll val, const ModInt<mod>& n) { return not(val == n); }
template <uint mod>
inline std::istream& operator>>(std::istream& is, ModInt<mod>& n)
{
uint v;
return is >> v, n = v, is;
}
template <uint mod>
std::ostream& operator<<(std::ostream& os, const ModInt<mod>& n) { return (os << n()); }
//!============================================================================!//
//! 8888ba.88ba dP a88888b. dP !//
//! 88 '8b '8b 88 d8' '88 88 !//
//! 88 88 88 .d8888b. .d888b88 88 .d8888b. 88d8b.d8b. 88d888b. !//
//! 88 88 88 88' '88 88' '88 88 88' '88 88''88''88 88' '88 !//
//! 88 88 88 88. .88 88. .88 Y8. .88 88. .88 88 88 88 88. .88 !//
//! dP dP dP '88888P' '88888P8 Y88888P' '88888P' dP dP dP 88Y8888' !//
//!============================================================================!//
template <uint mod>
class ModComb
{
public:
ModComb(const std::size_t N) : f(N + 1, ModInt<mod>(1)), in(N + 1, ModInt<mod>(1)), invf(N + 1, ModInt<mod>(1))
{
for (uint i = 2; i <= N; i++) { f[i] = f[i - 1] * i, in[i] = (mod - (mod / i)) * in[mod % i], invf[i] = invf[i - 1] * in[i]; }
}
ModInt<mod> fact(const std::size_t N) const { return f[N]; }
ModInt<mod> inv(const std::size_t N) const { return in[N]; }
ModInt<mod> invFact(const std::size_t N) const { return invf[N]; }
ModInt<mod> perm(const std::size_t N, const std::size_t K) const { return N > f.size() or K > N ? ModInt<mod>(0) : f[N] * invf[N - K]; }
ModInt<mod> comb(const std::size_t N, const std::size_t K) const { return N > f.size() or K > N ? ModInt<mod>(0) : f[N] * invf[K] * invf[N - K]; }
private:
std::vector<ModInt<mod>> f, in, invf;
};
//!============================================!//
//! 8888ba.88ba oo !//
//! 88 '8b '8b !//
//! 88 88 88 .d8888b. dP 88d888b. !//
//! 88 88 88 88' '88 88 88' '88 !//
//! 88 88 88 88. .88 88 88 88 !//
//! dP dP dP '88888P8 dP dP dP !//
//!============================================!//
int main()
{
ll N, K;
std::cin >> N >> K;
using mint = ModInt<MOD>;
ModComb<MOD> mod(N);
mint ans = mod.perm(N, K) * N * (N + 1) / 2 - N * K * mod.fact(N - 1) * mod.invFact(N - K);
for (ll i = N - 1; i >= 1; i--) { ans -= i * (K * mod.fact(N - 1) * mod.invFact(N - K) - mod.comb(K, 2) * mod.fact(N - 2) * mod.invFact(N - K)); }
std::cout << ans << std::endl;
return 0;
}