結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー nvt4s
提出日時 2019-06-13 11:55:04
言語 C++14
(gcc 8.3.0)
結果
RE   .
実行時間 -
コード長 3,516 Byte
コンパイル時間 1,612 ms
使用メモリ 819,064 KB
最終ジャッジ日時 2019-08-23 00:00:05

ソースコード

diff #
#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 <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#endif

using namespace std;

#define rep(i, n) for(int i = 0; i < n; i++)
#define revrep(i, n) for(int i = n-1; i >= 0; i--)
typedef long long ll;
typedef pair<int,int> Pint;
typedef pair<ll, ll> P;
typedef vector<ll> vec;
typedef vector<vec> mat;
//typedef pair<int, pair<int, int>> P;
//typedef tuple<int,int,int> T;
ll INFL = 1000000000000000010;//10^18 = 2^60
int INF = 1000000000;//10^9
ll MOD  = 1000000007;
//vector<int> dy = {0,0,1,-1};
//vector<int> dx = {1,-1,0,0};

mat mul_mat(mat &A, mat &B){
  mat res(A.size(), vec(B[0].size()));
  rep(i, A.size())rep(k, B.size())rep(j, B[0].size()){
    res[i][j] = (res[i][j] + (A[i][k] * B[k][j]) % MOD) % MOD;
  }
  return res;
}
mat pow_mat(mat &A, ll n){
  mat res(A.size(), vec(A.size()));
  rep(i, A.size()) res[i][i] = 1;
  while(n > 0){
    if(n&1) res = mul_mat(res, A);
    A = mul_mat(A, A);
    n >>= 1;
  }
  return res;
}

int main(void){
  ll N, K;
  cin >> N >> K;
  vec A(N);
  rep(i, N) cin >> A[i];

  if(K <= N){
    cout << A[K] << " ";
    ll S = 0;
    rep(i, K){
      S = (S + A[i]) % MOD;
    }
    cout << S << endl;
    return 0;
  }
  if(N >= 50){
    mat a(N, vec(N, 0));
    rep(i, N) a[i][0] = 1;
    rep(i, N-1) a[i][i+1] = 1;
    mat a_ = a;
    a = pow_mat(a, K-N);
    ll F = 0;
    rep(i, N){
      F = (F + A[N-1-i] * a[i][0]) % MOD;
    }
    mat b(2*N, vec(2*N, 0));
    rep(i, N)rep(j, N){
      b[i][j] = a_[i][j];
      if(i == j){
        b[i+N][i] = 1;
        b[i+N][i+N] = 1;
      }
    }
    b = pow_mat(b, K-N+1);
    b[N][0]--;

    ll S = 0;
    rep(i, N){
      S = (S + A[N-1-i] * (b[i+N][0])) % MOD;
      S = (S + A[i]) % MOD;
    }
    S = (S + MOD) % MOD;
    cout << F << " " << S << endl;
    return 0;
  }

  vec F(K, 0);
  rep(i, N) F[i] = A[i];
  for(int i = 0; i < N; i++){
    F[N] += A[i];
  }
  for(int i = N+1; i < K; i++){
    F[i] = 2 * F[i-1] - F[i-N-1];
  }
  ll S = 0;
  rep(i, K){
    S += F[i];
  }
  cout << F[K-1] << " " << S << endl;


}
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