solution.h

/*
Code generated by https://github.com/goodstudyqaq/leetcode-local-tester
*/
#if __has_include("../utils/cpp/help.hpp")
#include "../utils/cpp/help.hpp"
#elif __has_include("../../utils/cpp/help.hpp")
#include "../../utils/cpp/help.hpp"
#else
#define debug(...) 42
#endif

template <typename T>
T inverse(T a, T m) {
    T u = 0, v = 1;
    while (a != 0) {
        T t = m / a;
        m -= t * a;
        swap(a, m);
        u -= t * v;
        swap(u, v);
    }
    assert(m == 1);
    return u;
}

template <typename T>
class Modular {
   public:
    using Type = typename decay<decltype(T::value)>::type;

    constexpr Modular() : value() {}
    template <typename U>
    Modular(const U& x) {
        value = normalize(x);
    }

    template <typename U>
    static Type normalize(const U& x) {
        Type v;
        if (-mod() <= x && x < mod())
            v = static_cast<Type>(x);
        else
            v = static_cast<Type>(x % mod());
        if (v < 0) v += mod();
        return v;
    }

    const Type& operator()() const { return value; }
    template <typename U>
    explicit operator U() const { return static_cast<U>(value); }
    constexpr static Type mod() { return T::value; }

    Modular& operator+=(const Modular& other) {
        if ((value += other.value) >= mod()) value -= mod();
        return *this;
    }
    Modular& operator-=(const Modular& other) {
        if ((value -= other.value) < 0) value += mod();
        return *this;
    }
    template <typename U>
    Modular& operator+=(const U& other) { return *this += Modular(other); }
    template <typename U>
    Modular& operator-=(const U& other) { return *this -= Modular(other); }
    Modular& operator++() { return *this += 1; }
    Modular& operator--() { return *this -= 1; }
    Modular operator++(int) {
        Modular result(*this);
        *this += 1;
        return result;
    }
    Modular operator--(int) {
        Modular result(*this);
        *this -= 1;
        return result;
    }
    Modular operator-() const { return Modular(-value); }

    template <typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
        uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
        uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
        asm(
            "divl %4; \n\t"
            : "=a"(d), "=d"(m)
            : "d"(xh), "a"(xl), "r"(mod()));
        value = m;
#else
        value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
        return *this;
    }
    template <typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) {
        long long q = static_cast<long long>(static_cast<long double>(value) * rhs.value / mod());
        value = normalize(value * rhs.value - q * mod());
        return *this;
    }
    template <typename U = T>
    typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
        value = normalize(value * rhs.value);
        return *this;
    }

    Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

    friend const Type& abs(const Modular& x) { return x.value; }

    template <typename U>
    friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);

    template <typename U>
    friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);

    template <typename V, typename U>
    friend V& operator>>(V& stream, Modular<U>& number);

   private:
    Type value;
};

template <typename T>
bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U>
bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U>
bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }

template <typename T>
bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U>
bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }

template <typename T>
bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }

template <typename T>
Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U>
Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }

template <typename T>
Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U>
Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }

template <typename T>
Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U>
Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }

template <typename T>
Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U>
Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }

template <typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
    assert(b >= 0);
    Modular<T> x = a, res = 1;
    U p = b;
    while (p > 0) {
        if (p & 1) res *= x;
        x *= x;
        p >>= 1;
    }
    return res;
}

template <typename T>
bool IsZero(const Modular<T>& number) {
    return number() == 0;
}

template <typename T>
string to_string(const Modular<T>& number) {
    return to_string(number());
}

// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
    return stream << number();
}

// U == std::istream? but done this way because of fastinput
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
    typename common_type<typename Modular<T>::Type, long long>::type x;
    stream >> x;
    number.value = Modular<T>::normalize(x);
    return stream;
}

/*
using ModType = int;

struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/

constexpr int md = 1e9 + 7;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

/*vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);

Mint C(int n, int k) {
  if (k < 0 || k > n) {
    return 0;
  }
  while ((int) fact.size() < n + 1) {
    fact.push_back(fact.back() * (int) fact.size());
    inv_fact.push_back(1 / fact.back());
  }
  return fact[n] * inv_fact[k] * inv_fact[n - k];
}*/

template <class T>
auto vect(const T& v, int n) { return vector<T>(n, v); }
template <class T, class... D>
auto vect(const T& v, int n, D... m) {
    return vector<decltype(vect(v, m...))>(n, vect(v, m...));
}

template <typename T>
static constexpr T inf = numeric_limits<T>::max() / 2;
mt19937_64 mrand(random_device{}());
long long rnd(long long x) { return mrand() % x; }
int lg2(long long x) { return sizeof(long long) * 8 - 1 - __builtin_clzll(x); }

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;

typedef pair<int, int> pii;
typedef tree<pii, null_type, less<pii>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

class Solution {
   public:
    int checkRecord(int n) {
        auto dp = vect(Mint(0), n + 2, 2);
        dp[0][0] = 1;
        for (int i = 1; i <= n + 1; i++) {
            for (int j = i - 1; j >= i - 3 && j >= 0; j--) {
                dp[i][0] += dp[j][0];
                dp[i][1] += dp[j][0] + dp[j][1];
            }
            // debug(i, dp[i][0], dp[i][1]);
        }
        return (int)dp[n + 1][1];
    }
};