結果

問題 No.1501 酔歩
コンテスト
ユーザー stoq
提出日時 2021-05-07 23:16:02
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 6,876 bytes
コンパイル時間 2,391 ms
コンパイル使用メモリ 207,924 KB
最終ジャッジ日時 2025-01-21 08:47:25
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 12 WA * 40 RE * 1
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 MOD_TYPE 1

#pragma region Macros

#include <bits/stdc++.h>
using namespace std;

#if 0
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
using Int = boost::multiprecision::cpp_int;
using lld = boost::multiprecision::cpp_dec_float_100;
#endif
#if 0
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
using ll = long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pld = pair<ld, ld>;
template <typename Q_type>
using smaller_queue = priority_queue<Q_type, vector<Q_type>, greater<Q_type>>;

constexpr ll MOD = (MOD_TYPE == 1 ? (ll)(1e9 + 7) : 998244353);
constexpr int INF = (int)1e9 + 10;
constexpr ll LINF = (ll)4e18;
constexpr ld PI = acos(-1.0);
constexpr ld EPS = 1e-7;
constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0};
constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0};

#define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i)
#define rep(i, n) REP(i, 0, n)
#define REPI(i, m, n) for (int i = m; i < (int)(n); ++i)
#define repi(i, n) REPI(i, 0, n)
#define MP make_pair
#define MT make_tuple
#define YES(n) cout << ((n) ? "YES" : "NO") << "\n"
#define Yes(n) cout << ((n) ? "Yes" : "No") << "\n"
#define possible(n) cout << ((n) ? "possible" : "impossible") << "\n"
#define Possible(n) cout << ((n) ? "Possible" : "Impossible") << "\n"
#define all(v) v.begin(), v.end()
#define NP(v) next_permutation(all(v))
#define dbg(x) cerr << #x << ":" << x << "\n";

struct io_init
{
  io_init()
  {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << setprecision(30) << setiosflags(ios::fixed);
  };
} io_init;
template <typename T>
inline bool chmin(T &a, T b)
{
  if (a > b)
  {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
inline bool chmax(T &a, T b)
{
  if (a < b)
  {
    a = b;
    return true;
  }
  return false;
}
inline ll CEIL(ll a, ll b)
{
  return (a + b - 1) / b;
}
template <typename A, size_t N, typename T>
inline void Fill(A (&array)[N], const T &val)
{
  fill((T *)array, (T *)(array + N), val);
}
template <typename T, typename U>
constexpr istream &operator>>(istream &is, pair<T, U> &p) noexcept
{
  is >> p.first >> p.second;
  return is;
}
template <typename T, typename U>
constexpr ostream &operator<<(ostream &os, pair<T, U> &p) noexcept
{
  os << p.first << " " << p.second;
  return os;
}
#pragma endregion

// --------------------------------------

#pragma region mint
template <int MOD>
struct Fp
{
  long long val;

  constexpr Fp(long long v = 0) noexcept : val(v % MOD)
  {
    if (val < 0)
      v += MOD;
  }

  constexpr int getmod()
  {
    return MOD;
  }

  constexpr Fp operator-() const noexcept
  {
    return val ? MOD - val : 0;
  }

  constexpr Fp operator+(const Fp &r) const noexcept
  {
    return Fp(*this) += r;
  }

  constexpr Fp operator-(const Fp &r) const noexcept
  {
    return Fp(*this) -= r;
  }

  constexpr Fp operator*(const Fp &r) const noexcept
  {
    return Fp(*this) *= r;
  }

  constexpr Fp operator/(const Fp &r) const noexcept
  {
    return Fp(*this) /= r;
  }

  constexpr Fp &operator+=(const Fp &r) noexcept
  {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }

  constexpr Fp &operator-=(const Fp &r) noexcept
  {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }

  constexpr Fp &operator*=(const Fp &r) noexcept
  {
    val = val * r.val % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }

  constexpr Fp &operator/=(const Fp &r) noexcept
  {
    long long a = r.val, 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);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }

  constexpr bool operator==(const Fp &r) const noexcept
  {
    return this->val == r.val;
  }

  constexpr bool operator!=(const Fp &r) const noexcept
  {
    return this->val != r.val;
  }

  friend constexpr ostream &operator<<(ostream &os, const Fp<MOD> &x) noexcept
  {
    return os << x.val;
  }

  friend constexpr istream &operator>>(istream &is, Fp<MOD> &x) noexcept
  {
    return is >> x.val;
  }
};

Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept
{
  if (n == 0)
    return 1;
  auto t = modpow(a, n / 2);
  t = t * t;
  if (n & 1)
    t = t * a;
  return t;
}

using mint = Fp<MOD>;
#pragma endregion

struct Q
{
  ll a, b;
  Q(ll aa = 0, ll bb = 1)
  {
    assert(bb != 0);
    ll g = gcd(abs(aa), abs(bb));
    a = aa / g, b = bb / g;
  }
  void reflesh()
  {
    ll g = gcd(abs(a), abs(b));
    a /= g, b /= g;
    if (a < 0 and b < 0)
      a *= -1, b *= -1;
  }
  Q &operator+=(Q q)
  {
    ll c = a * q.b + q.a * b;
    ll d = b * q.b;
    a = c, b = d;
    reflesh();
    return *this;
  }
  Q operator+(Q q)
  {
    return Q(*this) += q;
  }
  Q &operator-=(Q q)
  {
    ll c = a * q.b - q.a * b;
    ll d = b * q.b;
    ll g = gcd(abs(c), abs(d));
    a = c / g, b = d / g;
    return *this;
  }
  Q &operator-(Q q)
  {
    return Q(*this) -= q;
  }
  Q &operator*=(Q q)
  {
    ll c = a * q.a;
    ll d = b * q.b;
    ll g = gcd(abs(c), abs(d));
    a = c / g, b = d / g;
    reflesh();
    return *this;
  }
  Q operator*(Q q)
  {
    return Q(*this) *= q;
  }
  Q &operator/=(Q q)
  {
    assert(q.a != 0);
    ll c = a * q.b;
    ll d = b * q.a;
    ll g = gcd(abs(c), abs(d));
    a = c / g, b = d / g;
    reflesh();
    return *this;
  }
  Q operator/(Q q)
  {
    return Q(*this) /= q;
  }
  bool operator==(Q q)
  {
    return a == q.a and b == q.b;
  }
  bool operator!=(Q q)
  {
    return !((*this) == q);
  }
};

void solve()
{
  int n, k;
  cin >> n >> k;
  k--;
  vector<int> a(n);
  rep(i, n) cin >> a[i];
  if (k == 0)
  {
    cout << 0 << "\n";
    return;
  }
  else if (k == n - 1)
  {
    cout << "1/1\n";
    return;
  }
  Q A(a[0], a[0] + a[2]), B(-1), C(a[2], a[0] + a[2]);
  for (int i = 2; i <= k; i++)
  {
    Q p(a[i - 1], a[i - 1] + a[i + 1]), q(-1), r(a[i + 1], a[i - 1] + a[i + 1]);
    Q k = B / p * Q(-1);
    p *= k, q *= k, r *= k;
    assert(B + p == Q(0));
    B = C + q, C = r;
  }
  Q D(a[n - 3], a[n - 1] + a[n - 3]), E(-1), F(a[n - 1], a[n - 1] + a[n - 3]);
  for (int i = n - 3; i >= k + 1; i--)
  {
    Q p(a[i - 1], a[i - 1] + a[i + 1]), q(-1), r(a[i + 1], a[i - 1] + a[i + 1]);
    Q k = E / r * Q(-1);
    p *= k, q *= k, r *= k;
    assert(E + r == Q(0));
    E = D + q, D = p;
  }
  if (k == n - 2)
  {
    Q ans = C / B * Q(-1);
    cout << ans.a << "/" << ans.b << "\n";
    return;
  }
  /*
  cout << D.a << "/" << D.b << "\n";
  cout << E.a << "/" << E.b << "\n";
  cout << F.a << "/" << F.b << "\n";*/
  Q t = C / E * Q(-1);
  D *= t, E *= t, F *= t;
  B += D, C += E;
  Q ans = F / B * Q(-1);
  cout << ans.a << "/" << ans.b << "\n";
}

int main()
{
  solve();
}
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