Problem p03717 (C++)

Buggy submission (status: Memory Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (ll i = 0; i < (n); ++i)
const ll MOD = 1e9 + 7;

template <uint_fast64_t Modulus> class modint {
  using u64 = uint_fast64_t;

public:
  u64 a;
  constexpr modint(const u64 x = 0) noexcept
      : a(((x % Modulus) + Modulus) % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr modint &operator+=(const modint &rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus)
      a -= Modulus;
    return *this;
  }
  constexpr modint operator+(const modint &rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint &operator++() noexcept { return ++a, *this; }
  constexpr modint operator++(int) noexcept {
    modint t = *this;
    return ++a, t;
  }
  constexpr modint &operator-=(const modint &rhs) noexcept {
    if (a < rhs.a)
      a += Modulus;
    a -= rhs.a;
    return *this;
  }
  constexpr modint operator-(const modint &rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint &operator--() noexcept { return --a, *this; }
  constexpr modint operator--(int) noexcept {
    modint t = *this;
    return --a, t;
  }
  constexpr modint &operator*=(const modint &rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint operator*(const modint &rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp & 1)
        *this *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return *this;
  }
  constexpr modint operator/(const modint &rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint operator-() const noexcept { return modint(Modulus - a); }
  constexpr bool operator==(const modint &rhs) const noexcept {
    return a == rhs.a;
  }
  constexpr bool operator!=(const modint &rhs) const noexcept {
    return a != rhs.a;
  }
  constexpr bool operator!() const noexcept { return !a; }
  friend constexpr modint pow(modint rhs, long long exp) noexcept {
    modint res{1};
    while (exp) {
      if (exp & 1)
        res *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return res;
  }
  friend ostream &operator<<(ostream &s, const modint &rhs) noexcept {
    return s << rhs.a;
  }
  friend istream &operator>>(istream &s, modint &rhs) noexcept {
    u64 a;
    rhs = modint{(s >> a, a)};
    return s;
  }
};

using mint = modint<MOD>;

const int MAX = 2e6 + 10;
vector<mint> fac(MAX), finv(MAX), inv(MAX);
void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; ++i) {
    fac[i] = fac[i - 1] * i;
    inv[i] = -inv[MOD % i] * (MOD / i);
    finv[i] = finv[i - 1] * inv[i];
  }
}
mint COM(int n, int k) {
  if (n < k || n < 0 || k < 0)
    return 0;
  return fac[n] * finv[k] * finv[n - k];
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int N, M;
  cin >> N >> M;
  struct condition {
    int l, r, x;
    condition(int l, int r, int x) : l(l), r(r), x(x) {}
    const bool operator<(const condition &rhs) { return r < rhs.r; }
  };
  vector<condition> C;
  rep(i, M) {
    int l, r, x;
    cin >> l >> r >> x;
    C.emplace_back(l, r, x);
  }
  sort(C.begin(), C.end());
  int s = 0, t = 0;
  mint dp[N + 1][N + 1][N + 1];
  rep(i, N + 1) rep(j, N + 1) rep(k, N + 1) dp[i][j][k] = 0;
  dp[0][0][0] = 1;
  rep(i, N + 1) {
    while (t < C.size() && C[t].r <= i)
      ++t;
    rep(j, N + 1) rep(k, N + 1) {
      for (int c = s; c < t; ++c) {
        int cnt = 0;
        if (C[c].l <= i && i <= C[c].r)
          ++cnt;
        if (C[c].l <= j && j <= C[c].r)
          ++cnt;
        if (C[c].l <= k && k <= C[c].r)
          ++cnt;
        if (cnt != C[c].x)
          dp[i][j][k] = 0;
      }
      if (i == N)
        continue;
      dp[i + 1][j][k] += dp[i][j][k];
      dp[i + 1][i][k] += dp[i][j][k];
      dp[i + 1][i][j] += dp[i][j][k];
    }
    s = t;
  }
  mint ans = 0;
  rep(j, N + 1) rep(k, N + 1) ans += dp[N][j][k];
  cout << ans << endl;
}

Fixed submission:
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (ll i = 0; i < (n); ++i)
const ll MOD = 1e9 + 7;

template <uint_fast64_t Modulus> class modint {
  using u64 = uint_fast64_t;

public:
  u64 a;
  constexpr modint(const u64 x = 0) noexcept
      : a(((x % Modulus) + Modulus) % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr modint &operator+=(const modint &rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus)
      a -= Modulus;
    return *this;
  }
  constexpr modint operator+(const modint &rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint &operator++() noexcept { return ++a, *this; }
  constexpr modint operator++(int) noexcept {
    modint t = *this;
    return ++a, t;
  }
  constexpr modint &operator-=(const modint &rhs) noexcept {
    if (a < rhs.a)
      a += Modulus;
    a -= rhs.a;
    return *this;
  }
  constexpr modint operator-(const modint &rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint &operator--() noexcept { return --a, *this; }
  constexpr modint operator--(int) noexcept {
    modint t = *this;
    return --a, t;
  }
  constexpr modint &operator*=(const modint &rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint operator*(const modint &rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp & 1)
        *this *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return *this;
  }
  constexpr modint operator/(const modint &rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint operator-() const noexcept { return modint(Modulus - a); }
  constexpr bool operator==(const modint &rhs) const noexcept {
    return a == rhs.a;
  }
  constexpr bool operator!=(const modint &rhs) const noexcept {
    return a != rhs.a;
  }
  constexpr bool operator!() const noexcept { return !a; }
  friend constexpr modint pow(modint rhs, long long exp) noexcept {
    modint res{1};
    while (exp) {
      if (exp & 1)
        res *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return res;
  }
  friend ostream &operator<<(ostream &s, const modint &rhs) noexcept {
    return s << rhs.a;
  }
  friend istream &operator>>(istream &s, modint &rhs) noexcept {
    u64 a;
    rhs = modint{(s >> a, a)};
    return s;
  }
};

using mint = modint<MOD>;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int N, M;
  cin >> N >> M;
  struct condition {
    int l, r, x;
    condition(int l, int r, int x) : l(l), r(r), x(x) {}
    const bool operator<(const condition &rhs) { return r < rhs.r; }
  };
  vector<condition> C;
  rep(i, M) {
    int l, r, x;
    cin >> l >> r >> x;
    C.emplace_back(l, r, x);
  }
  sort(C.begin(), C.end());
  int s = 0, t = 0;
  mint dp[N + 1][N + 1][N + 1];
  rep(i, N + 1) rep(j, N + 1) rep(k, N + 1) dp[i][j][k] = 0;
  dp[0][0][0] = 1;
  rep(i, N + 1) {
    while (t < C.size() && C[t].r <= i)
      ++t;
    rep(j, N + 1) rep(k, N + 1) {
      for (int c = s; c < t; ++c) {
        int cnt = 0;
        if (C[c].l <= i && i <= C[c].r)
          ++cnt;
        if (C[c].l <= j && j <= C[c].r)
          ++cnt;
        if (C[c].l <= k && k <= C[c].r)
          ++cnt;
        if (cnt != C[c].x)
          dp[i][j][k] = 0;
      }
      if (i == N)
        continue;
      dp[i + 1][j][k] += dp[i][j][k];
      dp[i + 1][i][k] += dp[i][j][k];
      dp[i + 1][i][j] += dp[i][j][k];
    }
    s = t;
  }
  mint ans = 0;
  rep(j, N + 1) rep(k, N + 1) ans += dp[N][j][k];
  cout << ans << endl;
}