結果
問題 | No.891 隣接3項間の漸化式 |
ユーザー |
|
提出日時 | 2019-09-20 21:37:41 |
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 | 7,678 bytes |
コンパイル時間 | 2,228 ms |
コンパイル使用メモリ | 197,328 KB |
最終ジャッジ日時 | 2025-01-07 18:41:39 |
ジャッジサーバーID (参考情報) |
judge2 / judge6 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 39 |
ソースコード
#include <bits/stdc++.h> #define LLI long long int #define FOR(v, a, b) for(LLI v = (a); v < (b); ++v) #define FORE(v, a, b) for(LLI v = (a); v <= (b); ++v) #define REP(v, n) FOR(v, 0, n) #define REPE(v, n) FORE(v, 0, n) #define REV(v, a, b) for(LLI v = (a); v >= (b); --v) #define ALL(x) (x).begin(), (x).end() #define RALL(x) (x).rbegin(), (x).rend() #define ITR(it, c) for(auto it = (c).begin(); it != (c).end(); ++it) #define RITR(it, c) for(auto it = (c).rbegin(); it != (c).rend(); ++it) #define EXIST(c,x) ((c).find(x) != (c).end()) #define fst first #define snd second #define popcount __builtin_popcount #define UNIQ(v) (v).erase(unique(ALL(v)), (v).end()) #define bit(i) (1LL<<(i)) #ifdef DEBUG #include <misc/C++/Debug.cpp> #else #define dump(...) ((void)0) #endif #define gcd __gcd using namespace std; template <class T> constexpr T lcm(T m, T n){return m/gcd(m,n)*n;} template <typename I> void join(ostream &ost, I s, I t, string d=" "){for(auto i=s; i!=t; ++i){if(i!=s)ost<<d; ost<<*i;}ost<<endl;} template <typename T> istream& operator>>(istream &is, vector<T> &v){for(auto &a : v) is >> a; return is;} template <typename T, typename U> bool chmin(T &a, const U &b){return (a>b ? a=b, true : false);} template <typename T, typename U> bool chmax(T &a, const U &b){return (a<b ? a=b, true : false);} template <typename T, size_t N, typename U> void fill_array(T (&a)[N], const U &v){fill((U*)a, (U*)(a+N), v);} struct Init{ Init(){ cin.tie(0); ios::sync_with_stdio(false); } }init; template <uint32_t M> class ModInt{ public: uint64_t val; ModInt(): val(0){} ModInt(int64_t n){ if(n >= M) val = n % M; else if(n < 0) val = n % M + M; else val = n; } inline constexpr ModInt operator+(const ModInt &a) const {return ModInt((val+a.val)%M);} inline constexpr ModInt operator-(const ModInt &a) const {return ModInt((val-a.val+M)%M);} inline constexpr ModInt operator*(const ModInt &a) const {return ModInt((val*a.val)%M);} inline constexpr ModInt operator/(const ModInt &a) const {return ModInt((val*a.inv().val)%M);} inline constexpr ModInt& operator=(const ModInt &a){val = a.val; return *this;} inline constexpr ModInt& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;} inline constexpr ModInt& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;} inline constexpr ModInt& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;} inline constexpr ModInt& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;} inline constexpr bool operator==(const ModInt &a) const {return val==a.val;} inline constexpr bool operator!=(const ModInt &a) const {return val!=a.val;} inline constexpr ModInt& operator++(){*this += 1; return *this;} inline constexpr ModInt& operator--(){*this -= 1; return *this;} inline constexpr ModInt operator++(int){ModInt t = *this; *this += 1; return t;} inline constexpr ModInt operator--(int){ModInt t = *this; *this -= 1; return t;} inline constexpr static ModInt power(LLI n, LLI p){ ModInt ret = 1, e = n; for(; p; e *= e, p >>= 1) if(p&1) ret *= e; return ret; } inline constexpr ModInt power(LLI p) const {return power(val,p);} inline constexpr ModInt inv() const { int64_t a = val, b = M, u = 1, v = 0; while(b){ int64_t t = a/b; a -= t*b; swap(a,b); u -= t*v; swap(u,v); } u %= M; if(u < 0) u += M; return u; } }; template <uint32_t M> ModInt<M> operator-(const ModInt<M> &a){return M-a.val;} template <uint32_t M> ModInt<M> operator+(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)+b.val);} template <uint32_t M> ModInt<M> operator-(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)-b.val);} template <uint32_t M> ModInt<M> operator*(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)*b.val);} template <uint32_t M> ModInt<M> operator/(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)/b.val);} template <uint32_t M> istream& operator>>(istream &is, ModInt<M> &a){is >> a.val; return is;} template <uint32_t M> ostream& operator<<(ostream &os, const ModInt<M> &a){ os << a.val; return os;} using mint = ModInt<1000000007>; template <typename T, int N> struct SquareMatrix{ array<array<T,N>,N> matrix; SquareMatrix(): matrix(){} SquareMatrix(const T &val){ REP(i,N) matrix[i].fill(val); } SquareMatrix(const SquareMatrix<T,N> &) = default; SquareMatrix(SquareMatrix<T,N> &&) = default; SquareMatrix(initializer_list<initializer_list<T>> list){ int i = 0; ITR(it1,list){ int j = 0; ITR(it2,*it1){ matrix[i][j] = *it2; ++j; } ++i; } } bool operator==(const SquareMatrix<T,N> &val) const { return matrix == val.matrix; } bool operator!=(const SquareMatrix<T,N> &val) const { return !(*this == val); } SquareMatrix& operator=(const SquareMatrix &) = default; SquareMatrix& operator+=(const SquareMatrix &val){ REP(i,N) REP(j,N) matrix[i][j] = matrix[i][j] + val[i][j]; return *this; } SquareMatrix& operator-=(const SquareMatrix &val){ REP(i,N) REP(j,N) matrix[i][j] = matrix[i][j] - val[i][j]; return *this; } SquareMatrix& operator*=(const SquareMatrix &val){ array<array<T,N>,N> temp = {}; REP(i,N) REP(j,N) REP(k,N) temp[i][j] = temp[i][j] + matrix[i][k] * val[k][j]; swap(matrix, temp); return *this; } inline const auto& operator[](size_t i) const {return matrix[i];} inline auto& operator[](size_t i){return matrix[i];} inline int size() const {return N;} static SquareMatrix<T,N> make_unit(){ SquareMatrix<T,N> ret; REP(i,N) ret[i][i] = 1; return ret; } SquareMatrix<T,N> transpose() const { SquareMatrix<T,N> ret; REP(i,N) REP(j,N) ret[i][j] = matrix[j][i]; return ret; } void show(int w = 10) const { #ifdef DEBUG cerr << "⎛" << string((w+1)*N, ' ') << "⎞" << endl; REP(i,N){ cerr << "⎜"; REP(j,N) cerr << setw(w) << matrix[i][j] << " "; cerr << "⎟"; cerr << endl; } cerr << "⎝" << string((w+1)*N, ' ') << "⎠" << endl; #endif } }; template <typename T, int N> SquareMatrix<T,N> operator+(const SquareMatrix<T,N> &a, const SquareMatrix<T,N> &b){auto ret = a; ret += b; return ret;} template <typename T, int N> SquareMatrix<T,N> operator-(const SquareMatrix<T,N> &a, const SquareMatrix<T,N> &b){auto ret = a; ret -= b; return ret;} template <typename T, int N> SquareMatrix<T,N> operator*(const SquareMatrix<T,N> &a, const SquareMatrix<T,N> &b){auto ret = a; ret *= b; return ret;} template <typename T, int N> SquareMatrix<T,N> power(SquareMatrix<T,N> a, uint64_t p){ if(p == 0) return SquareMatrix<T,N>::make_unit(); if(p == 1) return a; SquareMatrix<T,N> temp = power(a, p/2); auto ret = temp * temp; if(p%2) ret *= a; return ret; } template <typename T, int N> vector<T> operator*(const SquareMatrix<T,N> &a, const vector<T> &b){ vector<T> ret(N); REP(i,N){ REP(j,N){ ret[i] += a[i][j] * b[j]; } } return ret; } template <typename T, int N> vector<T> operator*(const vector<T> &b, const SquareMatrix<T,N> &a){ vector<T> ret(N); REP(i,N){ REP(j,N){ ret[j] += b[i] * a[i][j]; } } return ret; } using M = SquareMatrix<mint,2>; int main(){ mint a,b; int n; while(cin >> a >> b >> n){ if(n == 0){ cout << 0 << endl; }else if(n == 1){ cout << 1 << endl; }else{ M m = {{a,b},{1,0}}; m = power(m, n-1); mint ans = m[0][0]; cout << ans << endl; } } return 0; }