[Hackerearth] Tile Permutation Paradox

Problem Link    : Tile Permutation Paradox
Category        : DP
Contest         : January Circuits '24

#include "bits/stdc++.h"
using namespace std;
#define int     long long int
#define endl    '\n'
 
template <const int32_t MOD> struct modint {
    int32_t value;
    modint() = default;
    modint(int32_t value_) : value(value_) {}
    inline modint<MOD> operator + (modint<MOD> other) const { int32_t c = this->value + other.value; return modint<MOD>(c >= MOD ? c - MOD : c); }
    inline modint<MOD> operator - (modint<MOD> other) const { int32_t c = this->value - other.value; return modint<MOD>(c <    0 ? c + MOD : c); }
    inline modint<MOD> operator * (modint<MOD> other) const { int32_t c = (int64_t)this->value * other.value % MOD; return modint<MOD>(c < 0 ? c + MOD : c); }
    inline modint<MOD> & operator += (modint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
    inline modint<MOD> & operator -= (modint<MOD> other) { this->value -= other.value; if (this->value < 0) this->value += MOD; return *this; }
    inline modint<MOD> & operator *= (modint<MOD> other) { this->value = (int64_t)this->value * other.value % MOD; if (this->value < 0) this->value += MOD; return *this; }
    inline modint<MOD> operator - () const { return modint<MOD>(this->value ? MOD - this->value : 0); }
    modint<MOD> pow(uint64_t k) const { modint<MOD> x = *this, y = 1; for (; k; k >>= 1) { if (k & 1) y *= x; x *= x; } return y; }
    modint<MOD> inv() const { return pow(MOD - 2); }  // MOD must be a prime
    inline modint<MOD> operator /  (modint<MOD> other) const { return *this *  other.inv(); }
    inline modint<MOD> operator /= (modint<MOD> other)       { return *this *= other.inv(); }
    inline bool operator == (modint<MOD> other) const { return value == other.value; }
    inline bool operator != (modint<MOD> other) const { return value != other.value; }
    inline bool operator < (modint<MOD> other) const { return value < other.value; }
    inline bool operator > (modint<MOD> other) const { return value > other.value; }
};
template <int32_t MOD> modint<MOD> operator * (int64_t value, modint<MOD> n) { return modint<MOD>(value) * n; }
template <int32_t MOD> modint<MOD> operator * (int32_t value, modint<MOD> n) { return modint<MOD>(value % MOD) * n; }
template <int32_t MOD> istream & operator >> (istream & in, modint<MOD> &n) { return in >> n.value; }
template <int32_t MOD> ostream & operator << (ostream & out, modint<MOD> n) { return out << n.value; }
 
const int mod = 1e9 + 7;
using mint = modint<mod>;
 
signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr); cout.tie(nullptr);
    cout.precision(12);
 
    bool FILEIO = true; string FILE = "in.txt";
    if (FILEIO and fopen(FILE.c_str(), "r")) {
        freopen(FILE.c_str(), "r", stdin);
    }
 
    int tc;
    cin >> tc;
    for (int tcase = 1; tcase <= tc; tcase++) {
        int n, x;
        cin >> n >> x;
        mint ans = 0;
        {
            vector<mint> dp(n + 1);
            vector<int> table(n + 1);
            function<mint(int)> Solve = [&](int r) {
                if (r > n) {
                    return mint(1);
                }
                mint &ret = dp[r];
                int &tab = table[r];
                if (tab) {
                    return ret;
                }
                tab = 1;
                ret = Solve(r + 1);
                if (r + x - 1 <= n) {
                    ret += Solve(r + x);
                }
                return ret;
            };
            ans += Solve(1);
        }
        {
            vector<vector<mint>> dp(n + 1, vector<mint>(2));
            vector<vector<int>> table(n + 1, vector<int>(2));
            function<mint(int, int)> Solve = [&](int r, int flag) {
                if (r > n) {
                    return mint(1);
                }
                mint &ret = dp[r][flag];
                int &tab = table[r][flag];
                if (tab) {
                    return ret;
                }
                tab = 1;
                ret = 0;
                if (flag == 0) {
                    ret += Solve(r + 1, flag);
                }
                if (r + x - 1 <= n) {
                    ret += Solve(r + x, 1);
                }
                return ret;
            };
            ans -= Solve(1, 0);
 
        }
        cout << ans << endl;
    }
}