結果
| 問題 |
No.673 カブトムシ
|
| コンテスト | |
| ユーザー |
 sntea
|
| 提出日時 | 2018-04-21 01:21:21 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 10,427 bytes |
| コンパイル時間 | 1,991 ms |
| コンパイル使用メモリ | 182,020 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-06-30 06:09:34 |
| 合計ジャッジ時間 | 2,668 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 14 |
ソースコード
#ifdef LOCAL111
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#define _USE_MATH_DEFINES
#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#if __cplusplus >= 201103L
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif
// C++
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <type_traits>
#include <typeindex>
#include <unordered_map>
#include <unordered_set>
#endif
const int INF = 1e9;
using namespace std;
template<typename T, typename U> ostream& operator<< (ostream& os, const pair<T,U>& p) { os << '(' << p.first << ' ' << p.second << ')'; return os; }
#define endl '\n'
#define ALL(a) (a).begin(),(a).end()
#define SZ(a) int((a).size())
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define REP(i,n) FOR(i,0,n)
#define RREP(i,n) for (int i=(n)-1;i>=0;i--)
#ifdef LOCAL111
#define DEBUG(x) cout<<#x<<": "<<(x)<<endl
template<typename T> void dpite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
#else
#define DEBUG(x) true
template<typename T> void dpite(T a, T b){ return; }
#endif
#define F first
#define S second
#define SNP string::npos
#define WRC(hoge) cout << "Case #" << (hoge)+1 << ": "
template<typename T> void pite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
template<typename T> bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;}
template<typename T> bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;}
typedef long long int LL;
typedef unsigned long long ULL;
typedef pair<int,int> P;
void ios_init(){
//cout.setf(ios::fixed);
//cout.precision(12);
#ifdef LOCAL111
return;
#endif
ios::sync_with_stdio(false); cin.tie(0);
}
#define EPS 1e-9
//library
template<typename T>
class Matrix {
public:
vector<vector<T> > v;
int n,m;
Matrix(int n){
this->n = this->m = n;
v.resize(n,vector<T>(n,0));
}
Matrix(int n, int m){
this -> n = n;
this -> m = m;
v.resize(n,vector<T>(m,0));
}
size_t size() const {
return v.size();
}
int row() const {
return n;
}
int col() const {
return m;
}
Matrix operator+ (Matrix x) const {
Matrix res(n,m);
for(int i = 0; i < n; i++){
for(int j = 0; j < m; j++){
res.v[i][j] = x.v[i][j]+v[i][j];
}
}
return res;
}
Matrix operator-(Matrix x) const {
Matrix res(n,m);
for(int i = 0; i < n; i++){
for(int j = 0; j < m; j++){
res.v[i][j] = v[i][j]-x.v[i][j];
}
}
}
Matrix operator*(Matrix x) const {
Matrix res(n,x.m);
for(int i = 0; i < n; i++){
for(int j = 0; j < x.m; j++){
for(int k = 0; k < m; k++){
res.v[i][j] += v[i][k]*x.v[k][j];
}
}
}
return res;
}
Matrix operator-() const {
Matrix res = *this;
for(int i = 0; i < (int)v.size(); ++i) {
for(int j = 0; j < (int)v[i].size(); ++j) {
res [i][j] *= -1;
}
}
return res;
}
vector<T> operator*(vector<T> x) const {
assert(x.size() == v.size());
vector<T> res(v.size());
for(int i = 0; i < n; i++){
T tmp = 0;
for(int j = 0; j < m; j++){
tmp += v[i][j]*x[j];
}
res[i] = tmp;
}
return res;
}
Matrix pow(long long x) const {
assert(n == m);
Matrix m = (*this);
Matrix res(n);
for(int i = 0; i < n; i++) res[i][i] = 1;
while(x != 0) {
if(x&1) {
res = res*m;
}
m = m*m;
x >>= 1;
}
return res;
}
vector<T>& operator[](int x){
return v[x];
}
const vector<T>& operator[](int x) const {
return v[x];
}
Matrix<T> inverse() const{
assert(n == m);
Matrix res(n);
for(int i = 0; i < n; ++i) {
res[i][i] = 1;
}
// vector<pair<int,int>> swap_log;
Matrix<T> mat = *this;
for(int k = 0; k < n; ++k) {
T max_val = abs(mat[k][k]);
int max_point = k;
for(int i = k+1; i < n; ++i) {
if(max_val < abs(mat[i][k])){
max_val = abs(mat[i][k]);
max_point = i;
}
}
swap(mat[k],mat[max_point]);
swap(res[k],res[max_point]);
// swap_log.emplace_back(k,max_point);
for(int i = k+1; i < n; ++i) {
T m = mat[i][k]/mat[k][k];
for(int j = 0; j < n; ++j) {
mat[i][j] -= m*mat[k][j];
res[i][j] -= m*res[k][j];
}
}
}
for(int k = n-1; k >= 0; --k) {
for(int i = 0; i < k; ++i) {
T m = mat[i][k]/mat[k][k];
for(int j = 0; j < n; ++j) {
// mat[i][j] -= mat[k][j]*m;
res[i][j] -= res[k][j]*m;
}
}
}
for(int i = 0; i < n; ++i) {
for(int j = 0; j < n; ++j) {
res[i][j] /= mat[i][i];
}
}
// for(auto&& e : swap_log) {
// swap(res[e.first],res[e.second]);
// }
return res;
}
T det() const {
Matrix<T> mat = *this;
T res = 1;
for(int k = 0; k < n; ++k) {
T max_val = abs(mat[k][k]);
int max_point = k;
for(int i = k+1; i < n; ++i) {
if(max_val < abs(mat[i][k])){
max_val = abs(mat[i][k]);
max_point = i;
}
}
swap(mat[k],mat[max_point]);
if(k != max_point) res *= -1;
for(int i = k+1; i < n; ++i) {
T m = mat[i][k]/mat[k][k];
for(int j = 0; j < n; ++j) {
mat[i][j] -= m*mat[k][j];
}
}
}
for(int i = 0; i < n; ++i) {
res *= mat[i][i];
}
return res;
}
pair<T, vector<T>> getMaxEigenvalue(int iterNum = 10) const {
assert(n == m);
vector<T> xk_(n, 1);
xk_ = (*this).pow(iterNum)*xk_;
auto xk = (*this)*xk_;
T xk_xk = 0, xk_xk_ = 0;
for(int i = 0; i < n; i++) {
xk_xk += xk[i]*xk[i];
xk_xk_ += xk[i]*xk_[i];
}
T xkAbs = sqrt(xk_xk);
auto res = xk;
for(auto&& e : res) {
e /= xkAbs;
}
return { xk_xk/xk_xk_, res };
}
void debug() const {
for(auto&& ee : v) {
for(auto&& e : ee) {
cout << e << ' ';
}
cout << endl;
}
cout << endl;
}
};
template<typename T>
Matrix<T> companion_pow(const Matrix<T>& A, long long m) {
assert(A.col() == A.row());
int n = A.col();
Matrix<T> u(1, n), Ak = A;
u[0][n-1] = 1;
while(m > 0) {
if(m&1) {
u = u*Ak;
}
Matrix<T> a(1, n);
for(int i = 0; i < n; ++i) {
a[0][i] = Ak[n-1][i];
}
a = a*Ak;
for(int i = n-1; i >= 0; --i) {
for(int j = 0; j < n; ++j) {
Ak[i][j] = a[0][j];
}
auto a00 = a[0][0];
for(int j = 0; j < n-1; ++j) {
a[0][j] = a[0][j+1]+A[0][j]*a00;
}
a[0][n-1] = A[0][n-1]*a00;
}
m >>= 1;
}
Matrix<T> res(n);
for(int i = n-1; i >= 0; --i) {
for(int j = 0; j < n; ++j) {
res[i][j] = u[0][j];
}
auto u00 = u[0][0];
for(int j = 0; j < n-1; ++j) {
u[0][j] = u[0][j+1]+A[0][j]*u00;
}
u[0][n-1] = A[0][n-1]*u00;
}
return res;
}
//libary
template<long long MOD>
class ModInt {
public:
const static long long mod = MOD;
long long x;
ModInt() {
x = 0;
}
ModInt(long long x) {
x %= mod;
this->x = x < 0 ? x+mod : x;
}
int get() const {
return (int)x;
}
ModInt &operator+=(ModInt that) {
if((x += that.get()) >= mod) x -= mod;
return *this;
}
ModInt &operator-=(ModInt that) {
if((x += mod-that.get()) >= mod) x -= mod;
return *this;
}
ModInt &operator*=(ModInt that) {
x = x*that.get()%mod;
return *this;
}
ModInt &operator/=(ModInt that) {
return *this *= that.inverse();
}
ModInt operator+(ModInt that) const {
return ModInt(*this) += that;
}
ModInt operator-(ModInt that) const {
return ModInt(*this) -= that;
}
ModInt operator*(ModInt that) const {
return ModInt(*this) *= that;
}
ModInt operator/(ModInt that) const {
return ModInt(*this) /= that;
}
ModInt inverse() const {
using std::swap;
long long a = x, b = mod, u = 1, v = 0;
while(b) {
long long t = a/b;
a -= t*b; swap(a,b);
u -= t*v; swap(u,v);
}
return ModInt(u);
}
ModInt pow(int n) const {
ModInt b = *this;
ModInt res = 1;
while(n != 0) {
if(n&1){
res *= b;
}
b *= b;
n >>= 1;
}
return res;
}
bool operator==(ModInt that) const { return x == that.get(); }
bool operator!=(ModInt that) const { return x != that.get(); }
ModInt operator-() const { return x == 0 ? 0 : ModInt(mod-x); }
};
template<long long MOD> ostream& operator<< (ostream& os, const ModInt<MOD>& m) { os << m.get(); return os; }
template<long long MOD> istream& operator>> (istream& is, ModInt<MOD>& m){ long long n; is >> n; m = n; return is;}
typedef ModInt<1000000007> mint;
typedef double Num;
typedef vector<Num> Vec;
typedef vector<Vec> Mat;
int mrank(Mat A) {
int n = A.size();
int m = A[0].size();
int ret = 0;
for(int i = 0; i < n; i ++) {
//DEBUG(i);
int pivot = i;
for(int j = i+1; j < n; j ++)
if(abs(A[pivot][i]) < abs(A[j][i])) pivot = j;
swap(A[i], A[pivot]);
if(abs(A[i][i]) < EPS) continue;
Num r = Num(1) / A[i][i];
for(int j = i+1; j < n; j ++) {
Num u = A[j][i] * r;
for(int k = n-1; k >= i; k --)
A[j][k] -= u * A[i][k];
}
}
for(int i = 0; i < n; i++){
if(abs(A[i][m-1]) > EPS) ret = i;
}
/*REP(i,n) pite(ALL(A[i]));
cout << endl;*/
return ret;
}
//libary
int main()
{
ios_init();
LL b, c, d;
while(cin >> b >> c >> d) {
Matrix<mint> m(2, 2);
m[0][0] = c;
m[0][1] = b;
m[1][1] = 1;
auto po = m.pow(d);
REP(i, 2) dpite(ALL(po[i]));
auto ans = (po*vector<mint>({b, 1}))[0];
cout << ans-mint(b) << endl;
}
return 0;
}