Language: C++

#include "bits/stdc++.h"

#define REP(i,n) for(ll i=0;i<ll(n);++i)
#define RREP(i,n) for(ll i=ll(n)-1;i>=0;--i)
#define FOR(i,m,n) for(ll i=m;i<ll(n);++i)
#define RFOR(i,m,n) for(ll i=ll(n)-1;i>=ll(m);--i)
#define ALL(v) (v).begin(),(v).end()
#define UNIQUE(v) v.erase(unique(ALL(v)),v.end());
#define INF 1000000001ll
#define MOD 1000000007ll
#define EPS 1e-9

constexpr int dx[8] = { 1,1,0,-1,-1,-1,0,1 };
constexpr int dy[8] = { 0,1,1,1,0,-1,-1,-1 };


using namespace std;

using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using vvi = vector<vi>;
using vvl = vector<vl>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

template <class T> bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } return false; }
template <class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; }

#include "bits/stdc++.h"
template<int mod, bool isPrime = false >
class  Mint {
	using ll = long long;
	bool dirty;
	ll value;
	static std::vector<Mint> fact;
	static std::vector<Mint> rfact;
public:
	constexpr Mint() : value(0), dirty(false) {};
	constexpr Mint(ll x) : value(x), dirty(true) {
		value %= mod;
		if (value < 0)value += mod;
	}
	constexpr Mint(const Mint& other) : value(other.value), dirty(other.dirty) {}

	ll& get() { return value; }
	ll get() const { return value; }

	constexpr Mint pow(ll n) {
		Mint ret(1), tmp(value);
		while (n) {
			if (n & 1)ret *= tmp;
			n >>= 1;
			tmp *= tmp;
		}
		return ret;
	}
	constexpr bool initialized() const {
		return dirty;
	}
	constexpr bool operator == (const Mint& a) const {
		return value == a.value;
	}
	constexpr bool operator != (const Mint& a) const {
		return value != a.value;
	}
	constexpr Mint& operator =(const Mint& a) {
		value = a.value;
		dirty = true;
		return *this;
	}
	constexpr Mint& operator +=(const Mint& a) {
		if ((value += a.value) >= mod)value -= mod;
		dirty = true;
		return *this;
	}
	constexpr Mint& operator -=(const Mint& a) {
		if ((value += mod - a.value) >= mod)value -= mod;
		dirty = true;
		return *this;
	}
	constexpr Mint& operator *=(const Mint& a) {
		value = value * a.value % mod;
		dirty = true;
		return *this;
	}

	constexpr Mint& operator /=(const Mint& a) {
		initialized = true;
		return *this *= inv(a);
	}
	constexpr Mint operator +(const Mint& a) const {
		return Mint(*this) += a;
	}
	constexpr Mint operator -(const Mint& a) const {
		return Mint(*this) -= a;
	}
	constexpr Mint operator *(const Mint& a) const {
		return Mint(*this) *= a;
	}
	constexpr Mint operator /(const Mint& a) const {
		return Mint(*this) /= a;
	}
	static constexpr void init_comb(int n) {
		Mint::fact.resize(n + 1);
		Mint::rfact.resize(n + 1);
		for (int i = 0; i < n; ++i) {
			Mint::fact[i + 1] = Mint::fact[i] * (i + 1);
		}
		rfact[n] = inv(fact[n]);
		for (int i = n - 1; i >= 0; --i) {
			Mint::rfact[i] = Mint::rfact[i + 1] * (i + 1);
		}
	}
	static constexpr Mint comb(int a, int b) {
		if (a < 0 || b < 0 || a>fact.size() || b>fact.size() || a < b)return Mint(0);
		return fact[a] * rfact[b] * rfact[a - b];
	}
};

template<int mod, bool isPrime> std::ostream& operator << (std::ostream& os, const Mint<mod, isPrime>& m) { os << m.get(); return os; }
template<int mod, bool isPrime> std::istream& operator >> (std::istream& is, Mint<mod, isPrime>& m) { is >> m.get();  return is; }

template<int mod>
constexpr Mint<mod, true> inv(const Mint<mod, true>& m) {
	long long a = m.get(), b = mod, u = 1, v = 0;
	while (b) {
		long long t = a / b;
		a -= t * b; std::swap(a, b);
		u -= t * v; std::swap(u, v);
	}
	return Mint<mod, true>(u);
}

template<int mod, bool isPrime>
constexpr Mint<mod, isPrime> operator +(long long lhs, const Mint<mod, isPrime>& a) {
	return Mint<mod, isPrime>(lhs + a.get());
}

template<int mod, bool isPrime>
constexpr Mint<mod, isPrime> operator -(long long lhs, const Mint<mod, isPrime>& a) {
	return Mint<mod, isPrime>(lhs - a.get());
}

template<int mod, bool isPrime>
constexpr Mint<mod, isPrime> operator *(long long lhs, const Mint<mod, isPrime>& a) {
	return Mint<mod, isPrime>(lhs % mod * a.get());
}


template<int mod>
constexpr Mint<mod, true> operator /(long long lhs, const Mint<mod, true>& a) {
	return Mint<mod, true>(lhs % mod * inv(a));
}

constexpr int default_mod = 1000000007;
using mint = Mint<default_mod, true>;

vector<vector<mint>> sum;
mint solve(vector<vector<mint>>& dp, int a, int b) {
	if (dp[a][b].initialized())return dp[a][b];
	mint res = 0;
	if (b == 0) {
		dp[a][b] = 1;
		return 1;
	}
	if (a > 0)res += solve(dp, a - 1, b);
	res += sum[b - 1][min(a, b - 1)];
	return dp[a][b] = res;

}
int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	int a, b;
	cin >> a >> b;
	mint::init_comb(a + b);
	sum.resize(a + 1, vector<mint>(b + 1));
	REP(i, a + 1)REP(j, min((ll)b + 1, i + 1))sum[i][j] = mint::comb(i, j);
	REP(i, a + 1)REP(j, b)sum[i][j + 1] += sum[i][j];
	vector<vector<mint>> dp(a + 1, vector<mint>(b + 1));
	mint ans = 0;

	for (int k = 0; k <= a; ++k) {
		for (int i = 0; i <= a - k; ++i) {
			if (a - k - i <= b - 1) {
				ans += mint::comb(b - 1, a - k - i) * solve(dp, i, a - k - i);
			}
		}
	}
	cout << ans << endl;
}


Compiler output:
/usr/bin/ld: /tmp/ccEq6wn6.o: warning: relocation against `_ZN4MintILi1000000007ELb1EE5rfactE' in read-only section `.text._ZN4MintILi1000000007ELb1EE4combEii[_ZN4MintILi1000000007ELb1EE4combEii]'
/usr/bin/ld: /tmp/ccEq6wn6.o: in function `Mint<1000000007, true>::init_comb(int)':
a.cc:(.text._ZN4MintILi1000000007ELb1EE9init_combEi[_ZN4MintILi1000000007ELb1EE9init_combEi]+0x19): undefined reference to `Mint<1000000007, true>::fact'
/usr/bin/ld: a.cc:(.text._ZN4MintILi1000000007ELb1EE9init_combEi[_ZN4MintILi1000000007ELb1EE9init_combEi]+0x33): undefined reference to `Mint<1000000007, true>::rfact'
/usr/bin/ld: a.cc:(.text._ZN4MintILi1000000007ELb1EE9init_combEi[_ZN4MintILi1000000007ELb1EE9init_combEi]+0x6b): undefined reference to `Mint<1000000007, true>::fact'
/usr/bin/ld: a.cc:(.text._ZN4MintILi1000000007ELb1EE9init_combEi[_ZN4MintILi1000000007ELb1EE9init_combEi]+0x9b): undefined reference to `Mint<1000000007, true>::fact'
/usr/bin/ld: a.cc:(.text._ZN4MintILi1000000007ELb1EE9init_combEi[_ZN4MintILi1000000007ELb1EE9init_combEi]+0xd0): undefined reference to `Mint<1000000007, true>::fact'
/usr/bin/ld: a.cc:(.text._ZN4MintILi1000000007ELb1EE9init_combEi[_ZN4MintILi1000000007ELb1EE9init_combEi]+0xf9): undefined reference to `Mint<1000000007, true>::rfact'
/usr/bin/ld: a.cc:(.text._ZN4MintILi1000000007ELb1EE9init_combEi[_ZN4MintILi1000000007ELb1EE9init_combEi]+0x148): undefined reference to `Mint<1000000007, true>::rfact'
/usr/bin/ld: a.cc:(.text._ZN4MintILi1000000007ELb1EE9init_combEi[_ZN4MintILi1000000007ELb1EE9init_combEi]+0x175): undefined reference to `Mint<1000000007, true>::rfact'
/usr/bin/ld: /tmp/ccEq6wn6.o: in function `Mint<1000000007, true>::comb(int, int)':
a.cc:(.text._ZN4MintILi1000000007ELb1EE4combEii[_ZN4MintILi1000000007ELb1EE4combEii]+0x2a): undefined reference to `Mint<1000000007, true>::fact'
/usr/bin/ld: a.cc:(.text._ZN4MintILi1000000007ELb1EE4combEii[_ZN4MintILi1000000007ELb1EE4combEii]+0x44): undefined reference to `Mint<1000000007, true>::fact'
/usr/bin/ld: a.cc:(.text._ZN4MintILi1000000007ELb1EE4combEii[_ZN4MintILi1000000007ELb1EE4combEii]+0x8e): undefined reference to `Mint<1000000007, true>::rfact'
/usr/bin/ld: a.cc:(.text._ZN4MintILi1000000007ELb1EE4combEii[_ZN4MintILi1000000007ELb1EE4combEii]+0xa8): undefined reference to `Mint<1000000007, true>::rfact'
/usr/bin/ld: a.cc:(.text._ZN4MintILi1000000007ELb1EE4combEii[_ZN4MintILi1000000007ELb1EE4combEii]+0xc2): undefined reference to `Mint<1000000007, true>::fact'
/usr/bin/ld: warning: creating DT_TEXTREL in a PIE
collect2: error: ld returned 1 exit status