結果
| 問題 | No.1706 Many Bus Stops (hard) |
| ユーザー |
 rniya
|
| 提出日時 | 2021-10-08 23:02:18 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 3 ms / 2,000 ms |
| コード長 | 14,005 bytes |
| コンパイル時間 | 2,762 ms |
| コンパイル使用メモリ | 202,260 KB |
| 最終ジャッジ日時 | 2025-01-24 23:11:57 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 41 |
ソースコード
#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()
template <typename T> istream& operator>>(istream& is, vector<T>& v) {
for (T& x : v) is >> x;
return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
}
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
os << '(' << p.first << ',' << p.second << ')';
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
}
return os;
}
template <int i, typename T> void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {
if (i) os << ',';
os << get<i>(t);
print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {
os << '{';
print_tuple<0, tuple<Args...>, Args...>(os, t);
return os << '}';
}
void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
cerr << head;
if (sizeof...(Tail) > 0) cerr << ", ";
debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...) \
cerr << " "; \
cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
cerr << " "; \
debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
template <class T> T ceil(T x, T y) {
assert(y >= 1);
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
assert(y >= 1);
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
if (a < b) {
a = b;
return true;
}
return false;
}
#pragma endregion
#include <cassert>
#include <cstdint>
#include <iostream>
template <uint64_t Modulus> class modint {
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
static_assert(Modulus < static_cast<uint32_t>(1) << 31, "Modulus must be less than 2**31");
static constexpr u32 mod = Modulus;
u32 v;
public:
constexpr modint(const i64 x = 0) noexcept : v(x < 0 ? mod - 1 - (-(x + 1) % mod) : x % mod) {}
constexpr u32& val() noexcept { return v; }
constexpr const u32& val() const noexcept { return v; }
constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; }
constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; }
constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; }
constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; }
constexpr modint& operator+=(const modint& rhs) noexcept {
v += rhs.v;
if (v >= mod) v -= mod;
return *this;
}
constexpr modint& operator-=(const modint& rhs) noexcept {
if (v < rhs.v) v += mod;
v -= rhs.v;
return *this;
}
constexpr modint& operator*=(const modint& rhs) noexcept {
v = (u64)v * rhs.v % mod;
return *this;
}
constexpr modint& operator/=(const modint& rhs) noexcept { return *this *= rhs.inv(); }
constexpr modint pow(long long n) const noexcept {
assert(0 <= n);
modint self(*this), res(1);
while (n > 0) {
if (n & 1) res *= self;
self *= self;
n >>= 1;
}
return res;
}
constexpr modint inv() const noexcept {
assert(*this != 0);
return pow(mod - 2);
}
constexpr modint& operator++() noexcept {
if (++v == mod) v = 0;
return *this;
}
constexpr modint& operator--() noexcept {
if (v == 0) v = mod;
return --v, *this;
}
constexpr modint operator++(int) noexcept {
modint t = *this;
return ++*this, t;
}
constexpr modint operator--(int) noexcept {
modint t = *this;
return --*this, t;
}
constexpr modint operator-() const noexcept { return modint(mod - v); }
template <class T> friend constexpr modint operator+(T x, modint y) noexcept { return modint(x) + y; }
template <class T> friend constexpr modint operator-(T x, modint y) noexcept { return modint(x) - y; }
template <class T> friend constexpr modint operator*(T x, modint y) noexcept { return modint(x) * y; }
template <class T> friend constexpr modint operator/(T x, modint y) noexcept { return modint(x) / y; }
constexpr bool operator==(const modint& rhs) const noexcept { return v == rhs.v; }
constexpr bool operator!=(const modint& rhs) const noexcept { return v != rhs.v; }
constexpr bool operator!() const noexcept { return !v; }
friend std::istream& operator>>(std::istream& s, modint& rhs) noexcept {
i64 v;
rhs = modint{(s >> v, v)};
return s;
}
friend std::ostream& operator<<(std::ostream& s, const modint& rhs) noexcept { return s << rhs.v; }
};
/**
* @brief modint
* @docs docs/modulo/modint.md
*/
#include <cassert>
#include <iostream>
#include <vector>
template <typename T> struct Matrix {
std::vector<std::vector<T>> A;
Matrix(size_t n, size_t m) : A(n, std::vector<T>(m, 0)) {}
Matrix(size_t n) : A(n, std::vector<T>(n, 0)) {}
size_t size() const { return A.size(); }
size_t height() const { return A.size(); }
size_t width() const { return A[0].size(); }
inline const std::vector<T>& operator[](int k) const { return A[k]; }
inline std::vector<T>& operator[](int k) { return A[k]; }
static Matrix I(size_t n) {
Matrix res(n);
for (size_t i = 0; i < n; i++) res[i][i] = 1;
return res;
}
Matrix& operator+=(const Matrix& B) {
size_t n = height(), m = width();
assert(n == B.height() && m == B.width());
for (size_t i = 0; i < n; i++) {
for (size_t j = 0; j < m; j++) {
(*this)[i][j] += B[i][j];
}
}
return *this;
}
Matrix& operator-=(const Matrix& B) {
size_t n = height(), m = width();
assert(n == B.height() && m == B.width());
for (size_t i = 0; i < n; i++) {
for (size_t j = 0; j < m; j++) {
(*this)[i][j] -= B[i][j];
}
}
return *this;
}
Matrix& operator*=(const Matrix& B) {
size_t n = height(), m = B.width(), p = width();
assert(p == B.height());
std::vector<std::vector<T>> C(n, std::vector<T>(m, 0));
for (size_t i = 0; i < n; i++) {
for (size_t k = 0; k < p; k++) {
for (size_t j = 0; j < m; j++) {
C[i][j] += (*this)[i][k] * B[k][j];
}
}
}
A.swap(C);
return *this;
}
Matrix& operator*=(const T& v) {
for (size_t i = 0; i < height(); i++) {
for (size_t j = 0; j < width(); j++) {
(*this)[i][j] *= v;
}
}
return *this;
}
Matrix& operator/=(const T& v) {
T inv = T(1) / v;
for (size_t i = 0; i < height(); i++) {
for (size_t j = 0; j < width(); j++) {
(*this)[i][j] *= inv;
}
}
return *this;
}
Matrix& operator^=(long long k) {
assert(0 <= k);
Matrix B = Matrix::I(size());
while (k > 0) {
if (k & 1) B *= *this;
*this *= *this;
k >>= 1;
}
A.swap(B.A);
return *this;
}
Matrix operator-() const {
Matrix res(height(), width());
for (size_t i = 0; i < height(); i++) {
for (size_t j = 0; j < width(); j++) {
res[i][j] = -(*this)[i][j];
}
}
return res;
}
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; }
Matrix operator*(const T& v) const { return Matrix(*this) *= v; }
Matrix operator/(const T& v) const { return Matrix(*this) /= v; }
Matrix operator^(const long long k) const { return Matrix(*this) ^= k; }
bool operator==(const Matrix& B) const {
assert(height() == B.height() && width() == B.width());
return A == B.A;
}
bool operator!=(const Matrix& B) const {
assert(height() == B.height() && width() == B.width());
return A != B.A;
}
Matrix transpose() const {
Matrix res(width(), height());
for (size_t i = 0; i < height(); i++) {
for (size_t j = 0; j < width(); j++) {
res[j][i] = (*this)[i][j];
}
}
return res;
}
T determinant() const {
assert(height() == width());
Matrix B(*this);
T res = 1;
for (size_t i = 0; i < height(); i++) {
int pivot = -1;
for (size_t j = i; j < height(); j++) {
if (B[j][i] != 0) {
pivot = j;
break;
}
}
if (pivot == -1) return 0;
if (pivot != (int)i) {
res *= -1;
std::swap(B[i], B[pivot]);
}
res *= B[i][i];
T inv = T(1) / B[i][i];
for (size_t j = 0; j < width(); j++) B[i][j] *= inv;
for (size_t j = i + 1; j < height(); j++) {
T a = B[j][i];
for (size_t k = 0; k < width(); k++) {
B[j][k] -= B[i][k] * a;
}
}
}
return res;
}
friend std::ostream& operator<<(std::ostream& os, const Matrix& p) {
size_t n = p.height(), m = p.width();
os << "[(" << n << " * " << m << " Matrix)";
os << "\n[columun sums: ";
for (size_t j = 0; j < m; j++) {
T sum = 0;
for (size_t i = 0; i < n; i++) sum += p[i][j];
;
os << sum << (j + 1 < m ? "," : "");
}
os << "]";
for (size_t i = 0; i < n; i++) {
os << "\n[";
for (size_t j = 0; j < m; j++) os << p[i][j] << (j + 1 < m ? "," : "");
os << "]";
}
os << "]\n";
return os;
}
};
/**
* @brief 行列ライブラリ
* @docs docs/linearalgebra/Matrix.md
*/
const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;
using mint = modint<MOD>;
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
int C, N, M;
cin >> C >> N >> M;
Matrix<mint> M1(6), M2(6);
mint invC = mint(1) / C;
M1[0][0] = invC;
M1[0][5] = 1;
M1[1][0] = invC * (C - 1);
M1[2][1] = 1;
M1[3][2] = 1;
M1[3][3] = invC;
M1[3][5] = C - 2;
M1[4][3] = invC;
M1[5][4] = 1;
M2[0][0] = 1;
M2[0][5] = 1;
M2[2][1] = 1;
M2[3][2] = 1;
M2[3][3] = 1;
M2[3][5] = C - 2;
M2[5][4] = 1;
Matrix<mint> M3 = M2 * M1;
M3 ^= N;
mint prob = M3[0][0];
mint ans = 1 - (1 - prob).pow(M);
cout << ans << '\n';
return 0;
}