結果

問題 No.3226 2×2行列累乗
ユーザー amentorimaru
提出日時 2025-08-08 22:48:24
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 7,560 bytes
コンパイル時間 3,878 ms
コンパイル使用メモリ 267,680 KB
実行使用メモリ 7,716 KB
最終ジャッジ日時 2025-08-08 22:48:30
合計ジャッジ時間 5,130 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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 * 27
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 ATCODER
#include <bit>
#include <cstdint>
#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <queue>
#include <cassert>
#include <unordered_map>
#include <unordered_set>
#include <math.h>
#include <climits>
#include <set>
#include <map>
#include <list>
#include <iterator>
#include <bitset>
#include <chrono>
#include <type_traits>
using namespace std;

using ll = long long;

#define FOR(i, a, b) for(ll i=(a); i<(b);i++)
#define REP(i, n) for(ll i=0; i<(n);i++)
#define ROF(i, a, b) for(ll i=(b-1); i>=(a);i--)
#define PER(i, n) for(ll i=n-1; i>=0;i--)
#define VL vector<ll>
#define VVL vector<vector<ll>>
#define VP vector< pair<ll,ll> >
#define VVP vector<vector<pair<ll,ll>>>
#define all(i) begin(i),end(i)
#define SORT(i) sort(all(i))
#define EXISTBIT(x,i) (((x>>i) & 1) != 0)
#define MP(a,b) make_pair(a,b)
#ifdef ATCODER
#include <atcoder/all>
using namespace atcoder;
using mint = modint1000000007;
using mint2 = modint998244353;
#endif
template<typename T = ll>
vector<T> read(size_t n) {
  vector<T> ts(n);
  for (size_t i = 0; i < n; i++) cin >> ts[i];
  return ts;
}

template<typename TV, const ll N> void read_tuple_impl(TV&) {}
template<typename TV, const ll N, typename Head, typename... Tail>
void read_tuple_impl(TV& ts) {
  get<N>(ts).emplace_back(*(istream_iterator<Head>(cin)));
  read_tuple_impl<TV, N + 1, Tail...>(ts);
}
template<typename... Ts> decltype(auto) read_tuple(size_t n) {
  tuple<vector<Ts>...> ts;
  for (size_t i = 0; i < n; i++) read_tuple_impl<decltype(ts), 0, Ts...>(ts);
  return ts;
}

template<typename T> T det2(array<T, 4> ar) { return ar[0] * ar[3] - ar[1] * ar[2]; }
template<typename T> T det3(array<T, 9> ar) { return ar[0] * ar[4] * ar[8] + ar[1] * ar[5] * ar[6] + ar[2] * ar[3] * ar[7] - ar[0] * ar[5] * ar[7] - ar[1] * ar[3] * ar[8] - ar[2] * ar[4] * ar[6]; }
template<typename T> bool chmax(T& tar, T src) { return tar < src ? tar = src, true : false; }
template<typename T> bool chmin(T& tar, T src) { return tar > src ? tar = src, true : false; }
template<typename T> void inc(vector<T>& ar) { for (auto& v : ar) v++; }
template<typename T> void dec(vector<T>& ar) { for (auto& v : ar) v--; }
template<typename T> vector<pair<T, int>> id_sort(vector<T>& a) {
  vector<T, int> res(a.size());
  for (int i = 0; i < a.size(); i++)res[i] = MP(a[i], i);
  SORT(res);
  return res;
}

using val = pair<mint2, ll>; using func = pair<mint2,bool>;

val op(val a, val b) {
  return MP(a.first + b.first, a.second + b.second);
}
val e() {
  return MP(0LL, 0LL);
}
val mp(func f, val a) {
  if (f.second) {
    return MP(a.second * f.first, a.second);
  }
  else {
    return a;
  }
}
func comp(func f, func g) { 
  if (!f.second)return g;
  return f;
}
func id() { return MP(0, false); }


// Rook
ll dxr[4] = { 1,0,-1,0 };
ll dyr[4] = { 0,1,0,-1 };
// Bishop
ll dxb[4] = { -1,-1,1,1 };
ll djb[4] = { -1,1,-1,1 };
// qween
ll dxq[8] = { 0,-1,-1,-1,0,1,1,1 };
ll dyq[8] = { -1,-1,0,1,1,1,0,-1 };

template<typename T = ll>
class Matrix {
public:
  Matrix(ll l, ll c = 1) {
    low = l;
    column = c;
    var.resize(l);
    for (ll i = 0; i < l; i++) {
      var[i].assign(c, T(0));
    }
  }

  T& operator()(int i, int j = 0) {
    return var[i][j];
  }

  Matrix<T> operator+=(Matrix<T> m) {
    for (ll i = 0; i < low; i++) {
      for (ll j = 0; j < column; j++) {
        var[i][j] += m(i, j);
      }
    }
    return *this;
  }

  Matrix<T> operator -() {
    for (ll i = 0; i < low; i++) {
      for (ll j = 0; j < column; j++) {
        var[i][j] *= T(-1);
      }
    }
    return *this;
  }

  Matrix<T> operator-=(Matrix<T> m) {
    *this += -m;
    return *this;
  }

  Matrix<T> operator*=(T s) {
    for (ll i = 0; i < low; i++) {
      for (ll j = 0; j < column; j++) {
        var[i][j] *= s;
      }
    }
    return *this;
  }

  Matrix<T> operator/=(T s) {
    for (ll i = 0; i < low; i++) {
      for (ll j = 0; j < column; j++) {
        var[i][j] /= s;
      }
    }
    return *this;
  }


  Matrix<T> operator+(Matrix<T> m) {
    Matrix<T> ans = *this;
    return ans += m;
  }

  Matrix<T> operator-(Matrix<T> m) {
    Matrix<T> ans = *this;
    return ans -= m;
  }

  Matrix<T> operator*(T s) {
    Matrix<T> ans = *this;
    return ans *= s;
  }

  Matrix<T> operator/(T s) {
    Matrix<T> ans = *this;
    return ans /= s;
  }

  Matrix<T> operator*(Matrix<T> m) {
    Matrix<T> ans(low, m.column);
    for (ll i = 0; i < low; i++) {
      for (ll j = 0; j < m.column; j++) {
        for (ll k = 0; k < m.low; k++) {
          ans.var[i][j] += ((var[i][k]) * (m(k, j)));
        }
      }
    }
    return ans;
  }

  Matrix<T> Gaussian() {
    auto ans = *this;
    vector<ll> f(column, -1);
    for (ll j = 0; j < column; j++) {
      for (ll i = 0; i < low; i++) {
        if (ans.var[i][j] == 0) continue;
        if (f[j] == -1) {
          bool ok = true;
          for (ll k = 0; k < j; k++) {
            ok = ok && i != f[k];
          }
          if (ok) {
            f[j] = i;
            break;
          }
        }
      }
      if (f[j] == -1) {
        continue;
      }
      T rev = 1 / ans(f[j], j);
      for (ll i = 0; i < low; i++) {
        if (ans.var[i][j] == 0)continue;
        if (i == f[j])continue;
        T mul = ans.var[i][j] * rev;
        for (ll k = j; k < column; k++) {
          ans.var[i][k] -= ans.var[f[j]][k] * mul;
        }
      }
    }
    return ans;
  }

  T Determinant() {
    auto g = Gaussian();
    T ans = 1;
    for (ll i = 0; i < low; i++) {
      ans *= g(i, i);
    }
    return ans;
  }

  Matrix<T> SubMatrix(ll lowS, ll lowC, ll colS, ll colC) {
    Matrix<T> ans(lowC, colC);
    for (ll i = 0; i < lowC; i++) {
      for (ll j = 0; j < colC; j++) {
        ans(i, j) = var[lowS + i][colS + j];
      }
    }
    return ans;
  }

  Matrix<T> Inverse() {
    Matrix<T> ex(low, column * 2);
    for (ll i = 0; i < low; i++) {
      ex(i, column + i) = T(1);
      for (ll j = 0; j < column; j++) {
        ex(i, j) = var[i][j];
      }
    }
    auto g = ex.Gaussian();
    auto s = g.SubMatrix(0, low, column, column);
    for (ll i = 0; i < low; i++) {
      if (g.var[i][i] == 0) {
        return Matrix<T>(0, 0);
      }
      T inv = 1 / g.var[i][i];
      for (ll j = 0; j < column; j++) {
        s(i, j) *= inv;
      }
    }
    return s;
  }

  vector<vector<T>> var;
  ll low;
  ll column;
};

template<typename T>
static Matrix<T> operator*(const T& t, const Matrix<T>& m) {
  return m * t;
}

ll k;

template<typename T>
T Power(T var, ll p) {
  var.var[0][0] %= k;
  var.var[1][0] %= k;
  var.var[0][1] %= k;
  var.var[1][1] %= k;
  if (p == 1)
    return var;
  T ans = Power(var * var, p >> 1);
  if (p & 1)
    ans = ans * var;;
  ans.var[0][0] %= k;
  ans.var[1][0] %= k;
  ans.var[0][1] %= k;
  ans.var[1][1] %= k;
  return ans;
}


void solve() {
  Matrix m(2, 2);
  m.var[0] = read(2);
  m.var[1] = read(2);
  ll s, t, n;
  cin >> s >> t >> n >> k;
  m.var[0][0] %= k;
  m.var[0][0] += k;
  m.var[0][0] %= k;
  m.var[1][0] %= k;
  m.var[1][0] += k;
  m.var[1][0] %= k;
  m.var[0][1] %= k;
  m.var[0][1] += k;
  m.var[0][1] %= k;
  m.var[1][1] %= k;
  m.var[1][1] += k;
  m.var[1][1] %= k;
  s %= k;
  t %= k;
  s += k;
  t += k;
  s %= k;
  t %= k;
  if (n == 0) {
    cout << s << " " << t;
    return;
  }
  auto mn = Power(m, n);
  ll al = mn.var[0][0] * s + mn.var[0][1] * t;
  ll ar = mn.var[1][0] * s + mn.var[1][1] * t;
  cout << al % k << " " << ar % k;

}


int main() {
  ll t = 1;
   // cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}
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