//#pragma GCC optimize("Ofast") //#pragma GCC optimize("unroll-loops") #include <bits/stdc++.h> using namespace std; using ll = long long; using ull = unsigned long long; using pii = pair<int, int>; template <class T> using V = vector<T>; template <class T> using VV = V<V<T>>; template <class T> V<T> make_vec(size_t a) { return V<T>(a); } template <class T, class... Ts> auto make_vec(size_t a, Ts... ts) { return V<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...)); } #define pb push_back #define eb emplace_back #define mp make_pair #define fi first #define se second #define rep(i, n) rep2(i, 0, n) #define rep2(i, m, n) for (int i = m; i < (n); i++) #define per(i, b) per2(i, 0, b) #define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--) #define ALL(c) (c).begin(), (c).end() #define SZ(x) ((int)(x).size()) constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); } template <class T, class U> void chmin(T& t, const U& u) { if (t > u) t = u; } template <class T, class U> void chmax(T& t, const U& u) { if (t < u) t = u; } template <class T> void mkuni(vector<T>& v) { sort(ALL(v)); v.erase(unique(ALL(v)), end(v)); } template <class T, class U> ostream& operator<<(ostream& os, const pair<T, U>& p) { os << "(" << p.first << "," << p.second << ")"; return os; } template <class T> ostream& operator<<(ostream& os, const vector<T>& v) { os << "{"; rep(i, v.size()) { if (i) os << ","; os << v[i]; } os << "}"; return os; } #ifdef LOCAL void debug_out() { cerr << endl; } template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) { cerr << " " << H; debug_out(T...); } #define debug(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif template <class T> void print(T x, int suc = 1) { cout << x; if (suc == 1) cout << "\n"; else if (suc == 2) cout << " "; } template <class T> void print(const vector<T>& v, int suc = 1) { for (int i = 0; i < v.size(); ++i) print(v[i], i == int(v.size()) - 1 ? suc : 2); } template <unsigned int MOD> struct ModInt { using uint = unsigned int; using ull = unsigned long long; using M = ModInt; uint v; ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); } M& set_norm(uint _v) { //[0, MOD * 2)->[0, MOD) v = (_v < MOD) ? _v : _v - MOD; return *this; } explicit operator bool() const { return v != 0; } explicit operator int() const { return v; } M operator+(const M& a) const { return M().set_norm(v + a.v); } M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); } M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); } M operator/(const M& a) const { return *this * a.inv(); } M& operator+=(const M& a) { return *this = *this + a; } M& operator-=(const M& a) { return *this = *this - a; } M& operator*=(const M& a) { return *this = *this * a; } M& operator/=(const M& a) { return *this = *this / a; } M operator-() const { return M() - *this; } M& operator++(int) { return *this = *this + 1; } M& operator--(int) { return *this = *this - 1; } M pow(ll n) const { if (n < 0) return inv().pow(-n); M x = *this, res = 1; while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } M inv() const { ll a = v, b = MOD, p = 1, q = 0, t; while (b != 0) { t = a / b; swap(a -= t * b, b); swap(p -= t * q, q); } return M(p); } friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; } friend istream& operator>>(istream& in, M& x) { ll v_; in >> v_; x = M(v_); return in; } bool operator<(const M& r) const { return v < r.v; } bool operator>(const M& r) const { return v < *this; } bool operator<=(const M& r) const { return !(r < *this); } bool operator>=(const M& r) const { return !(*this < r); } bool operator==(const M& a) const { return v == a.v; } bool operator!=(const M& a) const { return v != a.v; } static uint get_mod() { return MOD; } }; using Mint = ModInt<1000000007>; // using Mint = ModInt<998244353>; V<Mint> fact, ifact, inv; void init() { const int maxv = 6000010; fact.resize(maxv); ifact.resize(maxv); inv.resize(maxv); fact[0] = 1; for (int i = 1; i < maxv; ++i) { fact[i] = fact[i - 1] * i; } ifact[maxv - 1] = fact[maxv - 1].inv(); for (int i = maxv - 2; i >= 0; --i) { ifact[i] = ifact[i + 1] * (i + 1); } for (int i = 1; i < maxv; ++i) { inv[i] = ifact[i] * fact[i - 1]; } } Mint comb(int n, int r) { if (n < 0 || r < 0 || r > n) return Mint(0); return fact[n] * ifact[r] * ifact[n - r]; } // O(k) Mint comb_slow(ll n, ll k) { Mint res = 1; for (int i = 0; i < k; ++i) { res = res * (n - i) * inv[i + 1]; } return res; } // line up // a 'o' + b 'x' Mint comb2(int a, int b) { if (b == 0) return (a == 0); return comb(a + b - 1, a); } // O(p + log_p n) Mint lucas(ll n, ll k, int p) { if (n < 0 || k < 0 || k > n) return Mint(0); Mint res = 1; while (n > 0) { res *= comb(n % p, k % p); n /= p; k /= p; } return res; } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); init(); int A, B, X, Y; cin >> A >> B >> X >> Y; Mint ans; int xp = B / 4 + 1, xn = (B >= 2 ? (B - 2) / 4 + 1 : 0); int yp = (B >= 1 ? (B - 1) / 4 + 1 : 0), yn = (B >= 2 ? (B - 2) / 4 + 1 : 0); rep(i, A + 1) { int j = A - i; if ((X + i) % 2) continue; if ((Y + j) % 2) continue; int a = (X + i) / 2; int b = i - a; int c = (Y + j) / 2; int d = j - c; if (!(0 <= a && a <= i) || !(0 <= c && c <= j)) continue; debug(a, b, c, d, xp, xn, yp, yn); ans += comb2(a, xp) * comb2(b, xn) * comb2(c, yp) * comb2(d, yn); } cout << ans << endl; return 0; }