結果
| 問題 | No.2365 Present of good number |
| ユーザー |
👑  emthrm
|
| 提出日時 | 2023-06-30 21:37:31 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 3 ms / 2,000 ms |
| コード長 | 8,677 bytes |
| コンパイル時間 | 2,832 ms |
| コンパイル使用メモリ | 276,784 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-07-07 09:15:18 |
| 合計ジャッジ時間 | 4,125 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 39 |
ソースコード
#include <bits/stdc++.h>using namespace std;#define FOR(i,m,n) for(int i=(m);i<(n);++i)#define REP(i,n) FOR(i,0,n)#define ALL(v) (v).begin(),(v).end()using ll = long long;constexpr int INF = 0x3f3f3f3f;constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;constexpr double EPS = 1e-8;// constexpr int MOD = 998244353;constexpr int MOD = 1000000007;constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};template <typename T, typename U>inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }template <typename T, typename U>inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }struct IOSetup {IOSetup() {std::cin.tie(nullptr);std::ios_base::sync_with_stdio(false);std::cout << fixed << setprecision(20);}} iosetup;template <unsigned int M>struct MInt {unsigned int v;constexpr MInt() : v(0) {}constexpr MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}static constexpr MInt raw(const int x) {MInt x_;x_.v = x;return x_;}static constexpr int get_mod() { return M; }static constexpr void set_mod(const int divisor) {assert(std::cmp_equal(divisor, M));}static void init(const int x) {inv<true>(x);fact(x);fact_inv(x);}template <bool MEMOIZES = false>static MInt inv(const int n) {// assert(0 <= n && n < M && std::gcd(n, M) == 1);static std::vector<MInt> inverse{0, 1};const int prev = inverse.size();if (n < prev) return inverse[n];if constexpr (MEMOIZES) {// "n!" and "M" must be disjoint.inverse.resize(n + 1);for (int i = prev; i <= n; ++i) {inverse[i] = -inverse[M % i] * raw(M / i);}return inverse[n];}int u = 1, v = 0;for (unsigned int a = n, b = M; b;) {const unsigned int q = a / b;std::swap(a -= q * b, b);std::swap(u -= q * v, v);}return u;}static MInt fact(const int n) {static std::vector<MInt> factorial{1};if (const int prev = factorial.size(); n >= prev) {factorial.resize(n + 1);for (int i = prev; i <= n; ++i) {factorial[i] = factorial[i - 1] * i;}}return factorial[n];}static MInt fact_inv(const int n) {static std::vector<MInt> f_inv{1};if (const int prev = f_inv.size(); n >= prev) {f_inv.resize(n + 1);f_inv[n] = inv(fact(n).v);for (int i = n; i > prev; --i) {f_inv[i - 1] = f_inv[i] * i;}}return f_inv[n];}static MInt nCk(const int n, const int k) {if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :fact_inv(n - k) * fact_inv(k));}static MInt nPk(const int n, const int k) {return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k);}static MInt nHk(const int n, const int k) {return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k));}static MInt large_nCk(long long n, const int k) {if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();inv<true>(k);MInt res = 1;for (int i = 1; i <= k; ++i) {res *= inv(i) * n--;}return res;}constexpr MInt pow(long long exponent) const {MInt res = 1, tmp = *this;for (; exponent > 0; exponent >>= 1) {if (exponent & 1) res *= tmp;tmp *= tmp;}return res;}constexpr MInt& operator+=(const MInt& x) {if ((v += x.v) >= M) v -= M;return *this;}constexpr MInt& operator-=(const MInt& x) {if ((v += M - x.v) >= M) v -= M;return *this;}constexpr MInt& operator*=(const MInt& x) {v = (unsigned long long){v} * x.v % M;return *this;}MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }constexpr auto operator<=>(const MInt& x) const = default;constexpr MInt& operator++() {if (++v == M) [[unlikely]] v = 0;return *this;}constexpr MInt operator++(int) {const MInt res = *this;++*this;return res;}constexpr MInt& operator--() {v = (v == 0 ? M - 1 : v - 1);return *this;}constexpr MInt operator--(int) {const MInt res = *this;--*this;return res;}constexpr MInt operator+() const { return *this; }constexpr MInt operator-() const { return raw(v ? M - v : 0); }constexpr MInt operator+(const MInt& x) const { return MInt(*this) += x; }constexpr MInt operator-(const MInt& x) const { return MInt(*this) -= x; }constexpr MInt operator*(const MInt& x) const { return MInt(*this) *= x; }MInt operator/(const MInt& x) const { return MInt(*this) /= x; }friend std::ostream& operator<<(std::ostream& os, const MInt& x) {return os << x.v;}friend std::istream& operator>>(std::istream& is, MInt& x) {long long v;is >> v;x = MInt(v);return is;}};using ModInt = MInt<MOD>;template <bool GETS_ONLY_PRIME>std::vector<int> prime_sieve(const int n) {std::vector<int> smallest_prime_factor(n + 1), prime;std::iota(smallest_prime_factor.begin(), smallest_prime_factor.end(), 0);for (int i = 2; i <= n; ++i) {if (smallest_prime_factor[i] == i) [[unlikely]] prime.emplace_back(i);for (const int p : prime) {if (i * p > n || p > smallest_prime_factor[i]) break;smallest_prime_factor[i * p] = p;}}return GETS_ONLY_PRIME ? prime : smallest_prime_factor;}struct OsaK {const std::vector<int> smallest_prime_factor;explicit OsaK(const int n) : smallest_prime_factor(prime_sieve<false>(n)) {}std::vector<std::pair<int, int>> query(int n) const {std::vector<std::pair<int, int>> res;while (n > 1) {const int prime = smallest_prime_factor[n];int exponent = 0;for (; smallest_prime_factor[n] == prime; n /= prime) {++exponent;}res.emplace_back(prime, exponent);}return res;}};template <typename T>struct Matrix {explicit Matrix(const int m, const int n, const T def = 0): data(m, std::vector<T>(n, def)) {}int nrow() const { return data.size(); }int ncol() const { return data.front().size(); }Matrix pow(long long exponent) const {const int n = nrow();Matrix<T> res(n, n, 0), tmp = *this;for (int i = 0; i < n; ++i) {res[i][i] = 1;}for (; exponent > 0; exponent >>= 1) {if (exponent & 1) res *= tmp;tmp *= tmp;}return res;}inline const std::vector<T>& operator[](const int i) const { return data[i]; }inline std::vector<T>& operator[](const int i) { return data[i]; }Matrix& operator=(const Matrix& x) = default;Matrix& operator+=(const Matrix& x) {const int m = nrow(), n = ncol();for (int i = 0; i < m; ++i) {for (int j = 0; j < n; ++j) {data[i][j] += x[i][j];}}return *this;}Matrix& operator-=(const Matrix& x) {const int m = nrow(), n = ncol();for (int i = 0; i < m; ++i) {for (int j = 0; j < n; ++j) {data[i][j] -= x[i][j];}}return *this;}Matrix& operator*=(const Matrix& x) {const int m = nrow(), l = ncol(), n = x.ncol();std::vector<std::vector<T>> res(m, std::vector<T>(n, 0));for (int i = 0; i < m; ++i) {for (int k = 0; k < l; ++k) {for (int j = 0; j < n; ++j) {res[i][j] += data[i][k] * x[k][j];}}}data.swap(res);return *this;}Matrix operator+(const Matrix& x) const { return Matrix(*this) += x; }Matrix operator-(const Matrix& x) const { return Matrix(*this) -= x; }Matrix operator*(const Matrix& x) const { return Matrix(*this) *= x; }private:std::vector<std::vector<T>> data;};int main() {using MIntEx = MInt<MOD - 1>;int n; ll k; cin >> n >> k;const OsaK osa_k(n + 1);map<int, MIntEx> pf;for (const auto& [p, e] : osa_k.query(n)) {pf.emplace(p, e);}for (; k > 0 && pf.rbegin()->first > 3; --k) {map<int, MIntEx> mp;for (const auto& [p, e] : pf) {for (const auto& [np, ne] : osa_k.query(p + 1)) mp[np] += e * ne;}pf.swap(mp);}if (k == 0) {ModInt ans = 1;for (const auto& [p, e] : pf) ans *= ModInt(p).pow(e.v);cout << ans << '\n';return 0;}Matrix<MIntEx> matrix(2, 2);matrix[0][1] = 2;matrix[1][0] = 1;matrix = matrix.pow(k);cout << ModInt(2).pow((matrix[0][0] * pf[2] + matrix[0][1] * pf[3]).v)* ModInt(3).pow((matrix[1][0] * pf[2] + matrix[1][1] * pf[3]).v)<< '\n';return 0;}