Problem p01511 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;
using Int = long long;
template <typename T1, typename T2> inline void chmin(T1 &a, T2 b) {
  if (a > b)
    a = b;
}
template <typename T1, typename T2> inline void chmax(T1 &a, T2 b) {
  if (a < b)
    a = b;
}

// BEGIN CUT HERE
template <size_t N, typename R> struct SquareMatrix {
  typedef array<R, N> arr;
  typedef array<arr, N> mat;
  mat dat;

  SquareMatrix() {
    for (size_t i = 0; i < N; i++)
      for (size_t j = 0; j < N; j++)
        dat[i][j] = R::add_identity();
  }
  SquareMatrix &operator=(const SquareMatrix &a) {
    dat = a.dat;
    return (*this);
  }
  bool operator==(const SquareMatrix &a) const { return dat == a.dat; }

  size_t size() const { return N; };
  arr &operator[](size_t k) { return dat[k]; };
  const arr &operator[](size_t k) const { return dat[k]; };

  static SquareMatrix add_identity() { return SquareMatrix(); }
  static SquareMatrix mul_identity() {
    SquareMatrix res;
    for (size_t i = 0; i < N; i++)
      res[i][i] = R::mul_identity();
    return res;
  }

  SquareMatrix operator*(const SquareMatrix &B) const {
    SquareMatrix res;
    for (size_t i = 0; i < N; i++)
      for (size_t j = 0; j < N; j++)
        for (size_t k = 0; k < N; k++)
          res[i][j] = res[i][j] + (dat[i][k] * B[k][j]);
    return res;
  }

  SquareMatrix operator+(const SquareMatrix &B) const {
    SquareMatrix res;
    for (size_t i = 0; i < N; i++)
      for (size_t j = 0; j < N; j++)
        res[i][j] = dat[i][j] + B[i][j];
    return res;
  }

  SquareMatrix pow(long long n) const {
    SquareMatrix a = *this, res = mul_identity();
    while (n) {
      if (n & 1)
        res = res * a;
      a = a * a;
      n >>= 1;
    }
    return res;
  }
};
// END CUT HERE

template <typename T, T MOD = 1000000007> struct Mint {
  T v;
  Mint() : v(0) {}
  Mint(signed v) : v(v) {}
  Mint(long long t) {
    v = t % MOD;
    if (v < 0)
      v += MOD;
  }

  Mint pow(long long k) {
    Mint res(1), tmp(v);
    while (k) {
      if (k & 1)
        res *= tmp;
      tmp *= tmp;
      k >>= 1;
    }
    return res;
  }

  static Mint add_identity() { return Mint(0); }
  static Mint mul_identity() { return Mint(1); }

  Mint inv() { return pow(MOD - 2); }

  Mint &operator+=(Mint a) {
    v += a.v;
    if (v >= MOD)
      v -= MOD;
    return *this;
  }
  Mint &operator-=(Mint a) {
    v += MOD - a.v;
    if (v >= MOD)
      v -= MOD;
    return *this;
  }
  Mint &operator*=(Mint a) {
    v = 1LL * v * a.v % MOD;
    return *this;
  }
  Mint &operator/=(Mint a) { return (*this) *= a.inv(); }

  Mint operator+(Mint a) const { return Mint(v) += a; };
  Mint operator-(Mint a) const { return Mint(v) -= a; };
  Mint operator*(Mint a) const { return Mint(v) *= a; };
  Mint operator/(Mint a) const { return Mint(v) /= a; };

  Mint operator-() { return v ? MOD - v : v; }

  bool operator==(const Mint a) const { return v == a.v; }
  bool operator!=(const Mint a) const { return v != a.v; }
  bool operator<(const Mint a) const { return v < a.v; }
};

struct FastIO {
  FastIO() {
    cin.tie(0);
    ios::sync_with_stdio(0);
  }
} fastio_beet;

template <typename T> vector<T> compress(vector<T> v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
  return v;
}

template <typename T> map<T, Int> dict(const vector<T> &v) {
  map<T, Int> res;
  for (Int i = 0; i < (Int)v.size(); i++)
    res[v[i]] = i;
  return res;
}

template <typename T, typename F> struct SegmentTree {
  Int n;
  F f;
  T ti;
  vector<T> dat;
  SegmentTree(){};
  SegmentTree(F f, T ti) : f(f), ti(ti) {}
  void init(Int n_) {
    n = 1;
    while (n < n_)
      n <<= 1;
    dat.assign(n << 1, ti);
  }
  void build(const vector<T> &v) {
    Int n_ = v.size();
    init(n_);
    for (Int i = 0; i < n_; i++)
      dat[n + i] = v[i];
    for (Int i = n - 1; i; i--)
      dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]);
  }
  void set_val(Int k, T x) {
    dat[k += n] = x;
    while (k >>= 1)
      dat[k] = f(dat[(k << 1) | 0], dat[(k << 1) | 1]);
  }
  T query(Int a, Int b) {
    T vl = ti, vr = ti;
    for (Int l = a + n, r = b + n; l < r; l >>= 1, r >>= 1) {
      if (l & 1)
        vl = f(vl, dat[l++]);
      if (r & 1)
        vr = f(dat[--r], vr);
    }
    return f(vl, vr);
  }
};

// INSERT ABOVE HERE
signed YAHOO2019_FINAL_D() {
  using M = Mint<Int>;
  using MM = SquareMatrix<2, M>;

  Int n, q;
  cin >> n >> q;
  vector<Int> ts(q), ls(q), rs(q), ps(q);
  for (Int i = 0; i < q; i++) {
    cin >> ts[i];
    if (ts[i] == 1)
      cin >> ps[i];
    if (ts[i] == 2)
      cin >> ls[i] >> rs[i];
  }
  vector<Int> vs;
  for (Int i = 0; i < q; i++) {
    if (ts[i] == 1) {
      vs.emplace_back(ps[i]);
      vs.emplace_back(ps[i] + 1);
      vs.emplace_back(ps[i] + 2);
      vs.emplace_back(ps[i] + 3);
    }
    if (ts[i] == 2) {
      vs.emplace_back(ls[i]);
      vs.emplace_back(ls[i] + 1);
      vs.emplace_back(rs[i]);
      vs.emplace_back(rs[i] + 1);
    }
  }
  vs.emplace_back(0);
  vs.emplace_back(n + 1);
  vs = compress(vs);
  auto ms = dict(vs);

  MM A;
  A[0][0] = M(1);
  A[0][1] = M(1);
  A[1][0] = M(1);
  A[1][1] = M(0);

  vector<MM> vt(vs.size() - 1, A);
  for (Int i = 0; i + 1 < (Int)vs.size(); i++) {
    vt[i] = A.pow(vs[i + 1] - vs[i]);
  }

  MM I = MM::mul_identity();
  auto f = [&](MM a, MM b) { return b * a; };
  SegmentTree<MM, decltype(f)> seg(f, I);
  seg.build(vt);

  vector<Int> used(vs.size(), 0);
  for (Int i = 0; i < q; i++) {
    if (ts[i] == 1) {
      Int k = ms[ps[i]];
      used[k] ^= 1;
      MM B;
      for (Int j = k; j <= k + 2; j++) {
        if (used[j]) {
          B[0][0] = M(0);
          B[0][1] = M(0);
          B[1][0] = M(1);
          B[1][1] = M(0);
        } else {
          B[0][0] = M(!used[j - 1]);
          B[0][1] = M(!used[j - 2]);
          B[1][0] = M(1);
          B[1][1] = M(0);
        }
        seg.set_val(j, B);
      }
    }
    if (ts[i] == 2) {
      Int l = ms[ls[i]], r = ms[rs[i]];
      if (used[l]) {
        cout << 0 << "\n";
        continue;
      }
      auto B = seg.query(l + 1, r + 1);
      cout << B[0][0].v << "\n";
    }
  }
  cout << flush;
  return 0;
}
/*
  verified on 2019/02/23
  https://atcoder.jp/contests/yahoo-procon2019-final/tasks/yahoo_procon2019_final_d
*/

signed DDCC2019_FINAL_D() {
  string s;
  cin >> s;

  struct M {
    uint32_t v;
    M() { *this = add_identity(); }
    M(uint32_t v) : v(v) {}
    M operator+(const M &a) const { return M(v + a.v); }
    M operator*(const M &a) const { return M(v * a.v); }
    static M add_identity() { return M(0); }
    static M mul_identity() { return M(1); }
  };

  using SM = SquareMatrix<6, M>;

  auto f = [](SM a, SM b) { return a * b; };
  SM ti = SM::mul_identity();
  SegmentTree<SM, decltype(f)> seg(f, ti);
  vector<SM> vt(s.size(), ti);
  for (int i = 0; i < (int)s.size(); i++) {
    if (s[i] == 'D')
      vt[i][0][1] = 1;
    if (s[i] == 'I')
      vt[i][1][2] = 1;
    if (s[i] == 'S')
      vt[i][2][3] = 1;
    if (s[i] == 'C')
      vt[i][3][4] = 1;
    if (s[i] == 'O')
      vt[i][4][5] = 1;
  }
  seg.build(vt);

  int q;
  cin >> q;
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    l--;
    cout << seg.query(l, r)[0][5].v << "\n";
  }
  cout << flush;
  return 0;
}
/*
  verified on 2019/02/23
  https://atcoder.jp/contests/ddcc2019-final/tasks/ddcc2019_final_d
*/

signed AOJ_2397() {
  const int MAX = 80;
  const int MOD = 1e9 + 9;
  using M = Mint<int, MOD>;
  using SM = SquareMatrix<MAX, M>;

  using ll = long long;
  ll w, h, n;
  ll cnt = 0;
  while (cin >> w >> h >> n, w) {
    vector<ll> x(n), y(n);
    for (int i = 0; i < n; i++)
      cin >> x[i] >> y[i];
    {
      using P = pair<ll, ll>;
      vector<P> vp;
      for (int i = 0; i < n; i++)
        vp.emplace_back(y[i], x[i]);
      sort(vp.begin(), vp.end());
      for (int i = 0; i < n; i++)
        tie(y[i], x[i]) = vp[i];
    }
    SM b;
    for (int i = 0; i < w; i++) {
      b[i][i] = M(1);
      if (i - 1 >= 0)
        b[i][i - 1] = M(1);
      if (i + 1 < w)
        b[i][i + 1] = M(1);
    }
    ll d = 1;
    SM res = SM::mul_identity();
    for (int k = 0; k < n; k++) {
      if (y[k] == d)
        continue;
      res = b.pow(y[k] - d - 1) * res;
      int j = k;
      SM c(b);
      while (j < n && y[k] == y[j]) {
        for (int i = 0; i < w; i++)
          c[x[j] - 1][i] = 0;
        j++;
      }
      res = c * res;
      d = y[k];
    }
    res = b.pow(h - d) * res;
    cout << "Case " << ++cnt << ": " << res[w - 1][0].v << endl;
  }
  return 0;
}
/*
  verified on 2019/04/11
  http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2397
*/

signed AOJ_2432() {
  const int MAX = 160;
  const int INF = 1e8;

  struct M {
    int v;
    M() { *this = add_identity(); }
    M(int v) : v(v) {}
    M operator+(const M &a) const { return M(max(v, a.v)); }
    M operator*(const M &a) const { return M(v + a.v); }
    static M add_identity() { return M(-INF); }
    static M mul_identity() { return M(0); }
  };
  using SM = SquareMatrix<MAX, M>;

  int n, m, k;
  cin >> n >> m >> k;
  vector<SM> vs(1), ws(1);

  for (int i = 0; i < n; i++) {
    vs[0][i][i] = 0;
    ws[0][i][i] = 0;
  }

  for (int i = 0; i < m; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    chmax(vs[0][a][b].v, c);
  }

  for (int t = 0; t < 20; t++) {
    SM tv = vs[t] * vs[t];
    SM tw = vs[t] * ws[t];
    vs.emplace_back(tv);
    ws.emplace_back(tw);
  }

  auto len = [&](SM &sm) -> int {
    int res = 0;
    for (int i = 0; i < n; i++)
      for (int j = 0; j < n; j++)
        chmax(res, sm[i][j].v);
    return res;
  };

  if (len(vs.back()) < k) {
    cout << -1 << endl;
    return 0;
  }

  int ans = 0;
  SM res(ws[0]);
  for (int t = 20; t >= 0; t--) {
    SM tmp = res * ws[t];
    SM nxt = res * vs[t];
    if (len(tmp) < k) {
      res.dat = nxt.dat;
      ans += 1 << t;
    }
  }
  cout << ans << endl;
  if (ans > 100)
    return 0;

  int dp[MAX][MAX];
  int pr[MAX][MAX];
  for (int i = 0; i < MAX; i++) {
    for (int j = 0; j < MAX; j++) {
      dp[i][j] = -INF;
      pr[i][j] = -1;
    }
  }
  for (int v = 0; v < n; v++)
    dp[0][v] = 0;
  for (int i = 0; i < ans; i++) {
    for (int v = 0; v < n; v++) {
      for (int u = 0; u < n; u++) {
        if (dp[i + 1][u] < dp[i][v] + vs[0][v][u].v) {
          dp[i + 1][u] = dp[i][v] + vs[0][v][u].v;
          pr[i + 1][u] = v;
        }
      }
    }
  }
  int pos = 0;
  for (int v = 0; v < n; v++)
    if (dp[ans][v] > dp[ans][pos])
      pos = v;

  vector<int> vx;
  for (int i = ans; i >= 0; i--) {
    vx.emplace_back(pos);
    pos = pr[i][pos];
  }
  reverse(vx.begin(), vx.end());
  for (int i = 0; i <= ans; i++) {
    if (i)
      cout << " ";
    cout << vx[i];
  }
  cout << endl;
  return 0;
}
/*
  verified on 2019/04/11
  http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2432
*/

signed main() {
  // YAHOO2019_FINAL_D();
  // DDCC2019_FINAL_D();
  AOJ_2397();
  // AOJ_2432();
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;
using Int = long long;
template <typename T1, typename T2> inline void chmin(T1 &a, T2 b) {
  if (a > b)
    a = b;
}
template <typename T1, typename T2> inline void chmax(T1 &a, T2 b) {
  if (a < b)
    a = b;
}

// BEGIN CUT HERE
template <size_t N, typename R> struct SquareMatrix {
  typedef array<R, N> arr;
  typedef array<arr, N> mat;
  mat dat;

  SquareMatrix() {
    for (size_t i = 0; i < N; i++)
      for (size_t j = 0; j < N; j++)
        dat[i][j] = R::add_identity();
  }
  SquareMatrix &operator=(const SquareMatrix &a) {
    dat = a.dat;
    return (*this);
  }
  bool operator==(const SquareMatrix &a) const { return dat == a.dat; }

  size_t size() const { return N; };
  arr &operator[](size_t k) { return dat[k]; };
  const arr &operator[](size_t k) const { return dat[k]; };

  static SquareMatrix add_identity() { return SquareMatrix(); }
  static SquareMatrix mul_identity() {
    SquareMatrix res;
    for (size_t i = 0; i < N; i++)
      res[i][i] = R::mul_identity();
    return res;
  }

  SquareMatrix operator*(const SquareMatrix &B) const {
    SquareMatrix res;
    for (size_t i = 0; i < N; i++)
      for (size_t j = 0; j < N; j++)
        for (size_t k = 0; k < N; k++)
          res[i][j] = res[i][j] + (dat[i][k] * B[k][j]);
    return res;
  }

  SquareMatrix operator+(const SquareMatrix &B) const {
    SquareMatrix res;
    for (size_t i = 0; i < N; i++)
      for (size_t j = 0; j < N; j++)
        res[i][j] = dat[i][j] + B[i][j];
    return res;
  }

  SquareMatrix pow(long long n) const {
    SquareMatrix a = *this, res = mul_identity();
    while (n) {
      if (n & 1)
        res = res * a;
      a = a * a;
      n >>= 1;
    }
    return res;
  }
};
// END CUT HERE

template <typename T, T MOD = 1000000007> struct Mint {
  T v;
  Mint() : v(0) {}
  Mint(signed v) : v(v) {}
  Mint(long long t) {
    v = t % MOD;
    if (v < 0)
      v += MOD;
  }

  Mint pow(long long k) {
    Mint res(1), tmp(v);
    while (k) {
      if (k & 1)
        res *= tmp;
      tmp *= tmp;
      k >>= 1;
    }
    return res;
  }

  static Mint add_identity() { return Mint(0); }
  static Mint mul_identity() { return Mint(1); }

  Mint inv() { return pow(MOD - 2); }

  Mint &operator+=(Mint a) {
    v += a.v;
    if (v >= MOD)
      v -= MOD;
    return *this;
  }
  Mint &operator-=(Mint a) {
    v += MOD - a.v;
    if (v >= MOD)
      v -= MOD;
    return *this;
  }
  Mint &operator*=(Mint a) {
    v = 1LL * v * a.v % MOD;
    return *this;
  }
  Mint &operator/=(Mint a) { return (*this) *= a.inv(); }

  Mint operator+(Mint a) const { return Mint(v) += a; };
  Mint operator-(Mint a) const { return Mint(v) -= a; };
  Mint operator*(Mint a) const { return Mint(v) *= a; };
  Mint operator/(Mint a) const { return Mint(v) /= a; };

  Mint operator-() { return v ? MOD - v : v; }

  bool operator==(const Mint a) const { return v == a.v; }
  bool operator!=(const Mint a) const { return v != a.v; }
  bool operator<(const Mint a) const { return v < a.v; }
};

struct FastIO {
  FastIO() {
    cin.tie(0);
    ios::sync_with_stdio(0);
  }
} fastio_beet;

template <typename T> vector<T> compress(vector<T> v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
  return v;
}

template <typename T> map<T, Int> dict(const vector<T> &v) {
  map<T, Int> res;
  for (Int i = 0; i < (Int)v.size(); i++)
    res[v[i]] = i;
  return res;
}

template <typename T, typename F> struct SegmentTree {
  Int n;
  F f;
  T ti;
  vector<T> dat;
  SegmentTree(){};
  SegmentTree(F f, T ti) : f(f), ti(ti) {}
  void init(Int n_) {
    n = 1;
    while (n < n_)
      n <<= 1;
    dat.assign(n << 1, ti);
  }
  void build(const vector<T> &v) {
    Int n_ = v.size();
    init(n_);
    for (Int i = 0; i < n_; i++)
      dat[n + i] = v[i];
    for (Int i = n - 1; i; i--)
      dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]);
  }
  void set_val(Int k, T x) {
    dat[k += n] = x;
    while (k >>= 1)
      dat[k] = f(dat[(k << 1) | 0], dat[(k << 1) | 1]);
  }
  T query(Int a, Int b) {
    T vl = ti, vr = ti;
    for (Int l = a + n, r = b + n; l < r; l >>= 1, r >>= 1) {
      if (l & 1)
        vl = f(vl, dat[l++]);
      if (r & 1)
        vr = f(dat[--r], vr);
    }
    return f(vl, vr);
  }
};

// INSERT ABOVE HERE
signed YAHOO2019_FINAL_D() {
  using M = Mint<Int>;
  using MM = SquareMatrix<2, M>;

  Int n, q;
  cin >> n >> q;
  vector<Int> ts(q), ls(q), rs(q), ps(q);
  for (Int i = 0; i < q; i++) {
    cin >> ts[i];
    if (ts[i] == 1)
      cin >> ps[i];
    if (ts[i] == 2)
      cin >> ls[i] >> rs[i];
  }
  vector<Int> vs;
  for (Int i = 0; i < q; i++) {
    if (ts[i] == 1) {
      vs.emplace_back(ps[i]);
      vs.emplace_back(ps[i] + 1);
      vs.emplace_back(ps[i] + 2);
      vs.emplace_back(ps[i] + 3);
    }
    if (ts[i] == 2) {
      vs.emplace_back(ls[i]);
      vs.emplace_back(ls[i] + 1);
      vs.emplace_back(rs[i]);
      vs.emplace_back(rs[i] + 1);
    }
  }
  vs.emplace_back(0);
  vs.emplace_back(n + 1);
  vs = compress(vs);
  auto ms = dict(vs);

  MM A;
  A[0][0] = M(1);
  A[0][1] = M(1);
  A[1][0] = M(1);
  A[1][1] = M(0);

  vector<MM> vt(vs.size() - 1, A);
  for (Int i = 0; i + 1 < (Int)vs.size(); i++) {
    vt[i] = A.pow(vs[i + 1] - vs[i]);
  }

  MM I = MM::mul_identity();
  auto f = [&](MM a, MM b) { return b * a; };
  SegmentTree<MM, decltype(f)> seg(f, I);
  seg.build(vt);

  vector<Int> used(vs.size(), 0);
  for (Int i = 0; i < q; i++) {
    if (ts[i] == 1) {
      Int k = ms[ps[i]];
      used[k] ^= 1;
      MM B;
      for (Int j = k; j <= k + 2; j++) {
        if (used[j]) {
          B[0][0] = M(0);
          B[0][1] = M(0);
          B[1][0] = M(1);
          B[1][1] = M(0);
        } else {
          B[0][0] = M(!used[j - 1]);
          B[0][1] = M(!used[j - 2]);
          B[1][0] = M(1);
          B[1][1] = M(0);
        }
        seg.set_val(j, B);
      }
    }
    if (ts[i] == 2) {
      Int l = ms[ls[i]], r = ms[rs[i]];
      if (used[l]) {
        cout << 0 << "\n";
        continue;
      }
      auto B = seg.query(l + 1, r + 1);
      cout << B[0][0].v << "\n";
    }
  }
  cout << flush;
  return 0;
}
/*
  verified on 2019/02/23
  https://atcoder.jp/contests/yahoo-procon2019-final/tasks/yahoo_procon2019_final_d
*/

signed DDCC2019_FINAL_D() {
  string s;
  cin >> s;

  struct M {
    uint32_t v;
    M() { *this = add_identity(); }
    M(uint32_t v) : v(v) {}
    M operator+(const M &a) const { return M(v + a.v); }
    M operator*(const M &a) const { return M(v * a.v); }
    static M add_identity() { return M(0); }
    static M mul_identity() { return M(1); }
  };

  using SM = SquareMatrix<6, M>;

  auto f = [](SM a, SM b) { return a * b; };
  SM ti = SM::mul_identity();
  SegmentTree<SM, decltype(f)> seg(f, ti);
  vector<SM> vt(s.size(), ti);
  for (int i = 0; i < (int)s.size(); i++) {
    if (s[i] == 'D')
      vt[i][0][1] = 1;
    if (s[i] == 'I')
      vt[i][1][2] = 1;
    if (s[i] == 'S')
      vt[i][2][3] = 1;
    if (s[i] == 'C')
      vt[i][3][4] = 1;
    if (s[i] == 'O')
      vt[i][4][5] = 1;
  }
  seg.build(vt);

  int q;
  cin >> q;
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    l--;
    cout << seg.query(l, r)[0][5].v << "\n";
  }
  cout << flush;
  return 0;
}
/*
  verified on 2019/02/23
  https://atcoder.jp/contests/ddcc2019-final/tasks/ddcc2019_final_d
*/

signed AOJ_2397() {
  const int MAX = 75;
  const int MOD = 1e9 + 9;
  using M = Mint<int, MOD>;
  using SM = SquareMatrix<MAX, M>;

  using ll = long long;
  ll w, h, n;
  ll cnt = 0;
  while (cin >> w >> h >> n, w) {
    vector<ll> x(n), y(n);
    for (int i = 0; i < n; i++)
      cin >> x[i] >> y[i];
    {
      using P = pair<ll, ll>;
      vector<P> vp;
      for (int i = 0; i < n; i++)
        vp.emplace_back(y[i], x[i]);
      sort(vp.begin(), vp.end());
      for (int i = 0; i < n; i++)
        tie(y[i], x[i]) = vp[i];
    }
    SM b;
    for (int i = 0; i < w; i++) {
      b[i][i] = M(1);
      if (i - 1 >= 0)
        b[i][i - 1] = M(1);
      if (i + 1 < w)
        b[i][i + 1] = M(1);
    }
    ll d = 1;
    SM res = SM::mul_identity();
    for (int k = 0; k < n; k++) {
      if (y[k] == d)
        continue;
      res = b.pow(y[k] - d - 1) * res;
      int j = k;
      SM c(b);
      while (j < n && y[k] == y[j]) {
        for (int i = 0; i < w; i++)
          c[x[j] - 1][i] = 0;
        j++;
      }
      res = c * res;
      d = y[k];
    }
    res = b.pow(h - d) * res;
    cout << "Case " << ++cnt << ": " << res[w - 1][0].v << endl;
  }
  return 0;
}
/*
  verified on 2019/04/11
  http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2397
*/

signed AOJ_2432() {
  const int MAX = 160;
  const int INF = 1e8;

  struct M {
    int v;
    M() { *this = add_identity(); }
    M(int v) : v(v) {}
    M operator+(const M &a) const { return M(max(v, a.v)); }
    M operator*(const M &a) const { return M(v + a.v); }
    static M add_identity() { return M(-INF); }
    static M mul_identity() { return M(0); }
  };
  using SM = SquareMatrix<MAX, M>;

  int n, m, k;
  cin >> n >> m >> k;
  vector<SM> vs(1), ws(1);

  for (int i = 0; i < n; i++) {
    vs[0][i][i] = 0;
    ws[0][i][i] = 0;
  }

  for (int i = 0; i < m; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    chmax(vs[0][a][b].v, c);
  }

  for (int t = 0; t < 20; t++) {
    SM tv = vs[t] * vs[t];
    SM tw = vs[t] * ws[t];
    vs.emplace_back(tv);
    ws.emplace_back(tw);
  }

  auto len = [&](SM &sm) -> int {
    int res = 0;
    for (int i = 0; i < n; i++)
      for (int j = 0; j < n; j++)
        chmax(res, sm[i][j].v);
    return res;
  };

  if (len(vs.back()) < k) {
    cout << -1 << endl;
    return 0;
  }

  int ans = 0;
  SM res(ws[0]);
  for (int t = 20; t >= 0; t--) {
    SM tmp = res * ws[t];
    SM nxt = res * vs[t];
    if (len(tmp) < k) {
      res.dat = nxt.dat;
      ans += 1 << t;
    }
  }
  cout << ans << endl;
  if (ans > 100)
    return 0;

  int dp[MAX][MAX];
  int pr[MAX][MAX];
  for (int i = 0; i < MAX; i++) {
    for (int j = 0; j < MAX; j++) {
      dp[i][j] = -INF;
      pr[i][j] = -1;
    }
  }
  for (int v = 0; v < n; v++)
    dp[0][v] = 0;
  for (int i = 0; i < ans; i++) {
    for (int v = 0; v < n; v++) {
      for (int u = 0; u < n; u++) {
        if (dp[i + 1][u] < dp[i][v] + vs[0][v][u].v) {
          dp[i + 1][u] = dp[i][v] + vs[0][v][u].v;
          pr[i + 1][u] = v;
        }
      }
    }
  }
  int pos = 0;
  for (int v = 0; v < n; v++)
    if (dp[ans][v] > dp[ans][pos])
      pos = v;

  vector<int> vx;
  for (int i = ans; i >= 0; i--) {
    vx.emplace_back(pos);
    pos = pr[i][pos];
  }
  reverse(vx.begin(), vx.end());
  for (int i = 0; i <= ans; i++) {
    if (i)
      cout << " ";
    cout << vx[i];
  }
  cout << endl;
  return 0;
}
/*
  verified on 2019/04/11
  http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2432
*/

signed main() {
  // YAHOO2019_FINAL_D();
  // DDCC2019_FINAL_D();
  AOJ_2397();
  // AOJ_2432();
  return 0;
}