結果
問題 | No.2365 Present of good number |
ユーザー |
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提出日時 | 2023-06-30 22:25:09 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 26 ms / 2,000 ms |
コード長 | 15,410 bytes |
コンパイル時間 | 2,712 ms |
コンパイル使用メモリ | 222,232 KB |
最終ジャッジ日時 | 2025-02-15 04:09:53 |
ジャッジサーバーID (参考情報) |
judge2 / judge5 |
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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
#line 1 "main.cpp"//#pragma GCC target("avx")//#pragma GCC optimize("O3")//#pragma GCC optimize("unroll-loops")#include<bits/stdc++.h>#ifdef LOCAL#include <debug.hpp>#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)#else#define debug(...) (static_cast<void>(0))#endifusing namespace std;using ll = long long;using ld = long double;using pll = pair<ll, ll>;using pii = pair<int, int>;using vi = vector<int>;using vvi = vector<vi>;using vvvi = vector<vvi>;using vl = vector<ll>;using vvl = vector<vl>;using vvvl = vector<vvl>;using vpii = vector<pii>;using vpll = vector<pll>;using vs = vector<string>;template<class T> using pq = priority_queue<T, vector<T>, greater<T>>;#define overload4(_1, _2, _3, _4, name, ...) name#define overload3(a,b,c,name,...) name#define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER)#define rep2(i, n) for (ll i = 0; i < (n); ++i)#define rep3(i, a, b) for (ll i = (a); i < (b); ++i)#define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c))#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)#define rrep1(n) for(ll i = (n) - 1;i >= 0;i--)#define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--)#define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--)#define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c)#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)#define all1(i) begin(i) , end(i)#define all2(i,a) begin(i) , begin(i) + a#define all3(i,a,b) begin(i) + a , begin(i) + b#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)#define sum(...) accumulate(all(__VA_ARGS__),0LL)template<class T> bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; }template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; }template<class T> auto min(const T& a){return *min_element(all(a));}template<class T> auto max(const T& a){return *max_element(all(a));}template<class... Ts> void in(Ts&... t);#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)#define LD(...) ld __VA_ARGS__; in(__VA_ARGS__)#define VEC(type, name, size) vector<type> name(size); in(name)#define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); in(name)ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;}ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }ll GCD(ll a,ll b) { if(a == 0 || b == 0) return 0; if(a % b == 0) return b; else return GCD(b,a%b);}ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;}namespace IO{#define VOID(a) decltype(void(a))struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(12);}} setting;template<int I> struct P : P<I-1>{};template<> struct P<0>{};template<class T> void i(T& t){ i(t, P<3>{}); }void i(vector<bool>::reference t, P<3>){ int a; i(a); t = a; }template<class T> auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; }template<class T> auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); }template<class T, size_t... idx> void ituple(T& t, index_sequence<idx...>){in(get<idx>(t)...);}template<class T> auto i(T& t, P<0>) -> VOID(tuple_size<T>{}){ituple(t, make_index_sequence<tuple_size<T>::value>{});}#undef VOID}#define unpack(a) (void)initializer_list<int>{(a, 0)...}template<class... Ts> void in(Ts&... t){ unpack(IO :: i(t)); }#undef unpackstatic const double PI = 3.1415926535897932;template <class F> struct REC {F f;REC(F &&f_) : f(forward<F>(f_)) {}template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }};constexpr int mod = 1000000007;//constexpr int mod = 998244353;#line 2 "library/modint/Modint.hpp"template <int mod>struct Modint{int x;Modint():x(0) {}Modint(long long y): x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}Modint &operator += (const Modint &p) {if((x += p.x) >= mod) x -= mod;return *this;}Modint &operator -= (const Modint &p) {if ((x += mod - p.x) >= mod) x -= mod;return *this;}Modint &operator *= (const Modint &p) {x = (int)(1LL * x * p.x % mod);return *this;}Modint &operator /= (const Modint &p) {*this *= p.inverse();return *this;}Modint operator -() const{return Modint(-x);}Modint operator +(const Modint &p) const {return Modint(*this) += p;}Modint operator -(const Modint &p) const {return Modint(*this) -= p;}Modint operator *(const Modint &p) const {return Modint(*this) *= p;}Modint operator /(const Modint &p) const {return Modint(*this) /= p;}Modint &operator ++() {if(x == mod - 1) x = 0; else x++; return *this;}Modint &operator --() {if(x == 0) x = mod - 1; else x--; return *this;}bool operator == (const Modint &p) const {return x == p.x;}bool operator != (const Modint &p) const {return x != p.x;}Modint inverse() const {int a = x, b = mod, u = 1, v = 0, t;while (b > 0) {t = a / b;swap(a -= t * b, b);swap(u -= t * v, v);}return Modint(u);}Modint pow(long long n) const {Modint ret(1), mul(x);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend ostream &operator<<(ostream &os, const Modint &p) { return os << p.x; }friend istream &operator>>(istream &is, Modint &a) {long long t;is >> t;a = Modint<mod>(t);return (is);}int get() const { return x; }static constexpr int get_mod() {return mod;}};#line 2 "library/modint/barrett-reduction.hpp"struct Barrett {using u32 = unsigned int;using i64 = long long;using u64 = unsigned long long;u32 m;u64 im;Barrett() : m(), im() {}Barrett(int n) : m(n), im(u64(-1) / m + 1) {}constexpr inline i64 quo(u64 n) {u64 x = u64((__uint128_t(n) * im) >> 64);u32 r = n - x * m;return m <= r ? x - 1 : x;}constexpr inline i64 rem(u64 n) {u64 x = u64((__uint128_t(n) * im) >> 64);u32 r = n - x * m;return m <= r ? r + m : r;}constexpr inline pair<i64, int> quorem(u64 n) {u64 x = u64((__uint128_t(n) * im) >> 64);u32 r = n - x * m;if (m <= r) return {x - 1, r + m};return {x, r};}constexpr inline i64 pow(u64 n, i64 p) {u32 a = rem(n), r = m == 1 ? 0 : 1;while (p) {if (p & 1) r = rem(u64(r) * a);a = rem(u64(a) * a);p >>= 1;}return r;}};#line 3 "library/modint/ArbitaryModint.hpp"struct ArbitraryModint {int x;ArbitraryModint():x(0) {}ArbitraryModint(int64_t y) {int z = y % get_mod();if(z < 0) z += get_mod();x = z;}ArbitraryModint &operator+=(const ArbitraryModint &p) {if((x += p.x) >= get_mod()) x -= get_mod();return *this;}ArbitraryModint &operator-=(const ArbitraryModint &p) {if((x += get_mod() - p.x) >= get_mod()) x -= get_mod();return *this;}ArbitraryModint &operator*=(const ArbitraryModint &p) {x = rem((unsigned long long)x * p.x);return *this;}ArbitraryModint &operator/=(const ArbitraryModint &p) {*this *= p.inverse();return *this;}ArbitraryModint operator-() const {return ArbitraryModint(-x);};ArbitraryModint operator+(const ArbitraryModint &p) const{return ArbitraryModint(*this) += p;}ArbitraryModint operator-(const ArbitraryModint &p) const{return ArbitraryModint(*this) -= p;}ArbitraryModint operator*(const ArbitraryModint &p) const{return ArbitraryModint(*this) *= p;}ArbitraryModint operator/(const ArbitraryModint &p) const {return ArbitraryModint(*this) /= p;}bool operator==(const ArbitraryModint &p) {return x == p.x;}bool operator!=(const ArbitraryModint &p) {return x != p.x;}ArbitraryModint inverse() const {int a = x,b = get_mod(),u = 1,v = 0,t;while(b > 0) {t = a / b;swap(a -= t * b,b);swap(u -= t * v,v);}return ArbitraryModint(u);}ArbitraryModint pow(int64_t n) const {ArbitraryModint ret(1),mul(x);while(n > 0) {if(n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend ostream &operator<<(ostream &os,const ArbitraryModint &p) {return os << p.x;}friend istream &operator>>(istream &is,ArbitraryModint &a) {int64_t t;is >> t;a = ArbitraryModint(t);return (is);}int get() const {return x;}inline unsigned int rem(unsigned long long p) {return barrett().rem(p);};static inline Barrett &barrett() {static Barrett b;return b;}static inline int &get_mod() {static int mod = 0;return mod;}static void set_mod(int md) {assert(0 < md && md <= (1LL << 30) - 1);get_mod() = md;barrett() = Barrett(md);}};#line 87 "main.cpp"using nmint = ArbitraryModint;using mint = Modint<mod>;using vm = vector<mint>;using vvm = vector<vm>;using vvvm = vector<vvm>;#line 2 "library/math/factorize.hpp"vector<pair<long long,int>> prime_factorization(long long n) {vector<pair<long long,int>> ret;int c = 0;while(n % 2 == 0) {c++;n >>= 1;}if(c) ret.emplace_back(2,c);for(long long i = 3; i * i <= n; i += 2) {c = 0;while(n % i == 0) {n /= i;c++;}if(c) ret.emplace_back(i,c);}if (n != 1) ret.emplace_back(n,1);return ret;}vector<long long> divisor(long long n) {vector<long long> ret;for(long long i = 1; i * i <= n; i++) {if (n % i == 0) {ret.push_back(i);if(i * i != n) {ret.push_back(n / i);}}}sort(ret.begin(),ret.end());return ret;}#line 2 "library/matrix/matrix.hpp"template <class T>struct Matrix {vector<vector<T>> A;Matrix() = default;Matrix(int n, int m) : A(n, vector<T>(m, T())) {}Matrix(int n) : A(n, vector<T>(n, T())){};int H() const { return A.size(); }int W() const { return A[0].size(); }int size() const { return A.size(); }inline const vector<T> &operator[](int k) const { return A[k]; }inline vector<T> &operator[](int k) { return A[k]; }static Matrix I(int n) {Matrix mat(n);for (int i = 0; i < n; i++) mat[i][i] = 1;return (mat);}Matrix &operator+=(const Matrix &B) {int n = H(), m = W();assert(n == B.H() && m == B.W());for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];return (*this);}Matrix &operator-=(const Matrix &B) {int n = H(), m = W();assert(n == B.H() && m == B.W());for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];return (*this);}Matrix &operator*=(const Matrix &B) {int n = H(), m = B.W(), p = W();assert(p == B.H());vector<vector<T>> C(n, vector<T>(m, T{}));for (int i = 0; i < n; i++)for (int k = 0; k < p; k++)for (int j = 0; j < m; j++) C[i][j] += (*this)[i][k] * B[k][j];A.swap(C);return (*this);}Matrix &operator^=(long long k) {Matrix B = Matrix::I(H());while (k > 0) {if (k & 1) B *= *this;*this *= *this;k >>= 1LL;}A.swap(B.A);return (*this);}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 long long k) const { return (Matrix(*this) ^= k); }bool operator==(const Matrix &B) const {assert(H() == B.H() && W() == B.W());for (int i = 0; i < H(); i++) for (int j = 0; j < W(); j++) {if (A[i][j] != B[i][j]) return false;}return true;}bool operator!=(const Matrix &B) const {assert(H() == B.H() && W() == B.W());for (int i = 0; i < H(); i++) for (int j = 0; j < W(); j++) {if (A[i][j] != B[i][j]) return true;}return false;}friend ostream &operator<<(ostream &os, const Matrix &p) {int n = p.H(), m = p.W();for (int i = 0; i < n; i++) {os << (i ? " " : "") << "[";for (int j = 0; j < m; j++) {os << p[i][j] << (j + 1 == m ? "]\n" : ",");}}return (os);}T determinant() const {Matrix B(*this);assert(H() == W());T ret = 1;for (int i = 0; i < H(); i++) {int idx = -1;for (int j = i; j < W(); j++) {if (B[j][i] != 0) {idx = j;break;}}if (idx == -1) return 0;if (i != idx) {ret *= T(-1);swap(B[i], B[idx]);}ret *= B[i][i];T inv = T(1) / B[i][i];for (int j = 0; j < W(); j++) {B[i][j] *= inv;}for (int j = i + 1; j < H(); j++) {T a = B[j][i];if (a == 0) continue;for (int k = i; k < W(); k++) {B[j][k] -= B[i][k] * a;}}}return ret;}};#line 94 "main.cpp"int main() {nmint::set_mod(mod - 1);INT(n);LL(k);auto ret = prime_factorization(n);vector<pair<int,nmint>> A;for(auto &[p,c]:ret) A.emplace_back(p,c);while(A.back().first > 3 && k > 0) {map<int,nmint> mp;for(auto &[p,c]:A) {auto tmp = prime_factorization(p + 1);for(auto &[pp,cc]:tmp) {mp[pp] += c * cc;}}A.clear();for(auto &x:mp) {A.emplace_back(x);}k--;}if(k == 0) {mint ans = 1;for(auto &[p,c]:A) {ans *= mint(p).pow(c.x);}cout << ans << '\n';return 0;}Matrix<nmint> mat(2);mat[0][1] = 1;mat[1][0] = 2;mat ^= k;vector<nmint> b(2);for(auto &[p,c]:A) {b[p-2] = c;}vector<nmint> cnt(2);rep(i,2) {rep(j,2) {cnt[i] += b[j] * mat[j][i];}}mint ans = 1;rep(i,2) ans *= mint(i+2).pow(cnt[i].x);cout << ans << '\n';}