結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー 👑 emthrmemthrm
提出日時 2021-04-14 05:57:04
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 9 ms / 5,000 ms
コード長 6,724 bytes
コンパイル時間 2,198 ms
コンパイル使用メモリ 202,376 KB
最終ジャッジ日時 2025-01-20 17:26:33
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 * 3
other AC * 37
権限があれば一括ダウンロードができます

ソースコード

diff # 

#define _USE_MATH_DEFINES
#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 = 1000000007;
// constexpr int MOD = 998244353;
constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, 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 <int M>
struct MInt {
  unsigned int val;
  MInt(): val(0) {}
  MInt(long long x) : val(x >= 0 ? x % M : x % M + M) {}
  static constexpr int get_mod() { return M; }
  static void set_mod(int divisor) { assert(divisor == M); }
  static void init(int x = 10000000) { inv(x, true); fact(x); fact_inv(x); }
  static MInt inv(int x, bool init = false) {
    // assert(0 <= x && x < M && std::__gcd(x, M) == 1);
    static std::vector<MInt> inverse{0, 1};
    int prev = inverse.size();
    if (init && x >= prev) {
      // "x!" and "M" must be disjoint.
      inverse.resize(x + 1);
      for (int i = prev; i <= x; ++i) inverse[i] = -inverse[M % i] * (M / i);
    }
    if (x < inverse.size()) return inverse[x];
    unsigned int a = x, b = M; int u = 1, v = 0;
    while (b) {
      unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }
  static MInt fact(int x) {
    static std::vector<MInt> f{1};
    int prev = f.size();
    if (x >= prev) {
      f.resize(x + 1);
      for (int i = prev; i <= x; ++i) f[i] = f[i - 1] * i;
    }
    return f[x];
  }
  static MInt fact_inv(int x) {
    static std::vector<MInt> finv{1};
    int prev = finv.size();
    if (x >= prev) {
      finv.resize(x + 1);
      finv[x] = inv(fact(x).val);
      for (int i = x; i > prev; --i) finv[i - 1] = finv[i] * i;
    }
    return finv[x];
  }
  static MInt nCk(int n, int k) {
    if (n < 0 || n < k || k < 0) return 0;
    if (n - k > k) k = n - k;
    return fact(n) * fact_inv(k) * fact_inv(n - k);
  }
  static MInt nPk(int n, int k) { return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k); }
  static MInt nHk(int n, int k) { return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k)); }
  static MInt large_nCk(long long n, int k) {
    if (n < 0 || n < k || k < 0) return 0;
    inv(k, true);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) res *= inv(i) * n--;
    return res;
  }
  MInt pow(long long exponent) const {
    MInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  MInt &operator+=(const MInt &x) { if((val += x.val) >= M) val -= M; return *this; }
  MInt &operator-=(const MInt &x) { if((val += M - x.val) >= M) val -= M; return *this; }
  MInt &operator*=(const MInt &x) { val = static_cast<unsigned long long>(val) * x.val % M; return *this; }
  MInt &operator/=(const MInt &x) { return *this *= inv(x.val); }
  bool operator==(const MInt &x) const { return val == x.val; }
  bool operator!=(const MInt &x) const { return val != x.val; }
  bool operator<(const MInt &x) const { return val < x.val; }
  bool operator<=(const MInt &x) const { return val <= x.val; }
  bool operator>(const MInt &x) const { return val > x.val; }
  bool operator>=(const MInt &x) const { return val >= x.val; }
  MInt &operator++() { if (++val == M) val = 0; return *this; }
  MInt operator++(int) { MInt res = *this; ++*this; return res; }
  MInt &operator--() { val = (val == 0 ? M : val) - 1; return *this; }
  MInt operator--(int) { MInt res = *this; --*this; return res; }
  MInt operator+() const { return *this; }
  MInt operator-() const { return MInt(val ? M - val : 0); }
  MInt operator+(const MInt &x) const { return MInt(*this) += x; }
  MInt operator-(const MInt &x) const { return MInt(*this) -= x; }
  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.val; }
  friend std::istream &operator>>(std::istream &is, MInt &x) { long long val; is >> val; x = MInt(val); return is; }
};
namespace std { template <int M> MInt<M> abs(const MInt<M> &x) { return x; } }
using ModInt = MInt<MOD>;

template <typename T>
T kita_masa(const std::vector<T> &c, const std::vector<T> &a, long long n) {
  if (n == 0) return a[0];
  int k = c.size();
  std::vector<T> coefficient[3];
  for (int i = 0; i < 3; ++i) coefficient[i].assign(k, 0);
  if (k == 1) {
    coefficient[0][0] = c[0] * a[0];
  } else {
    coefficient[0][1] = 1;
  }
  auto succ = [&c, k, &coefficient]() -> void {
    for (int i = 0; i < k - 1; ++i) coefficient[0][i] += coefficient[0].back() * c[i + 1];
    coefficient[0].back() *= c[0];
    std::rotate(coefficient[0].begin(), coefficient[0].begin() + k - 1, coefficient[0].end());
  };
  for (int bit = 62 - __builtin_clzll(n); bit >= 0; --bit) {
    for (int i = 1; i < 3; ++i) std::copy(coefficient[0].begin(), coefficient[0].end(), coefficient[i].begin());
    for (T &e : coefficient[1]) e *= coefficient[2][0];
    for (int i = 1; i < k; ++i) {
      succ();
      for (int j = 0; j < k; ++j) coefficient[1][j] += coefficient[2][i] * coefficient[0][j];
    }
    coefficient[0].swap(coefficient[1]);
    if (n >> bit & 1) succ();
  }
  T res = 0;
  for (int i = 0; i < k; ++i) res += coefficient[0][i] * a[i];
  return res;
}

int main() {
  int n;
  long long k;
  std::cin >> n >> k;
  --k;
  std::vector<ModInt> a(n);
  for (int i = 0; i < n; ++i) std::cin >> a[i];
  if (2 <= n && n <= 10000 && n <= k && k < 1000000) {
    ModInt sum = std::accumulate(a.begin(), a.end(), ModInt(0));
    a.resize(k + 1);
    for (int i = n; i <= k; ++i) {
      a[i] = sum;
      sum = sum + a[i] - a[i - n];
    }
    std::cout << a[k] << ' ' << std::accumulate(a.begin(), a.end(), ModInt(0)) << '\n';
  } else {
    std::cout << kita_masa(std::vector<ModInt>(n, 1), a, k) << ' ';
    // S(K) = 2S(K - 1) - S(K - (N + 1))
    std::vector<ModInt> c(n + 1, 0);
    c[0] = -1;
    c[n] = 2;
    a.emplace_back(std::accumulate(a.begin(), a.end(), ModInt(0)));
    for (int i = 1; i < n + 1; ++i) a[i] += a[i - 1];
    std::cout << kita_masa(c, a, k) << '\n';
  }
  return 0;
}
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