#include #include #include #include template struct mod_int { constexpr static signed MODULO = M; constexpr static size_t MAX_FACT = F; signed x; mod_int() : x(0) {} mod_int(long long y) : x(static_cast(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO)) { } mod_int(int y) : x(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO) { } mod_int &operator+=(const mod_int &rhs) { if ((x += rhs.x) >= MODULO) x -= MODULO; return *this; } mod_int &operator-=(const mod_int &rhs) { if ((x += MODULO - rhs.x) >= MODULO) x -= MODULO; return *this; } mod_int &operator*=(const mod_int &rhs) { x = static_cast(1LL * x * rhs.x % MODULO); return *this; } mod_int &operator/=(const mod_int &rhs) { assert(rhs.x != 0); x = static_cast((1LL * x * rhs.inv().x) % MODULO); return *this; } mod_int operator-() const { return mod_int(-x); } mod_int operator+(const mod_int &rhs) const { return mod_int(*this) += rhs; } mod_int operator-(const mod_int &rhs) const { return mod_int(*this) -= rhs; } mod_int operator*(const mod_int &rhs) const { return mod_int(*this) *= rhs; } mod_int operator/(const mod_int &rhs) const { return mod_int(*this) /= rhs; } bool operator<(const mod_int &rhs) const { return x < rhs.x; } mod_int inv() const { signed a = x, b = MODULO, u = 1, v = 0, t; while (b) { t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } return mod_int(u); } mod_int pow(long long t) const { assert(!(x == 0 && t == 0)); mod_int e = *this, res = mod_int(1); for (; t; e *= e, t >>= 1) if (t & 1) res *= e; return res; } mod_int fact() { if (_fact[0].x == 0) prepare(); return _fact[x]; } mod_int choose(mod_int y) { assert(y.x <= x); return this->fact() / y.fact() / (*this - y).fact(); } static mod_int _fact[MAX_FACT + 1]; static mod_int _inv_fact[MAX_FACT + 1]; static void prepare() { _fact[0] = 1; for (int i = 1; i <= MAX_FACT; ++i) { _fact[i] = _fact[i - 1] * i; } _inv_fact[MAX_FACT] = _fact[MAX_FACT].inv(); for (int i = (int) MAX_FACT - 1; i >= 0; --i) { _inv_fact[i] = _inv_fact[i + 1] * (i + 1); } } }; template std::ostream &operator<<(std::ostream &os, const mod_int &rhs) { return os << rhs.x; } template std::istream &operator>>(std::istream &is, mod_int &rhs) { long long s; is >> s; rhs = mod_int(s); return is; }; template mod_int mod_int::_fact[MAX_FACT + 1]; template mod_int mod_int::_inv_fact[MAX_FACT + 1]; template bool operator == (const mod_int &lhs, const mod_int &rhs) { return lhs.x == rhs.x; } template bool operator != (const mod_int &lhs, const mod_int &rhs) { return !(lhs == rhs); } const int MF = 3010; const int MOD = 1000000007; using mint = mod_int; mint binom(int n, int r) { return (r < 0 || r > n || n < 0) ? 0 : mint(n).choose(r); } mint fact(int n) { return mint(n).fact(); } using namespace std; // K = R + G + B // K = 1 + 2 + 2 + 2 + 1 + ... // f(i) := 2がi個,1がk-2i個あるのを並べる // g(i) := R,G,Bから色が違うペアをi個 // ans += f(i)G(i) using ll = long long; ll N, R, G, B; ll K; ll naive() { vector a; if (N < K) return 0; for (int i = 0; i < N - K; ++i) { a.push_back(0); } for (int i = 0; i < R; ++i) { a.push_back(1); } for (int j = 0; j < G; ++j) { a.push_back(2); } for (int k = 0; k < B; ++k) { a.push_back(3); } int ans = 0; do { bool ok = true; for (int i = 0; i < N - 1; ++i) { if (a[i] && a[i + 1] && a[i] == a[i + 1]) { ok = false; break; } if (i + 2 != N && a[i] && a[i + 1] && a[i + 2]) { ok = false; break; } } if (ok) { ++ans; } } while (next_permutation(a.begin(), a.end())); return ans; } mint pow2[3010]; mint f(ll single, ll pair) { mint res = 1; ll space = N - (pair * 2 + single); if (space < 0) return 0; res *= binom(single + pair, single); ll p = single + pair; ll q = N - (2 * pair + single); res *= binom(q + 1, p); return res; } mint g(ll single, ll pair) { mint res = 0; for (ll r = pair - min(G, B); r <= min({pair, R, G + B}); ++r) { int single_r = R - r; int single_g = G - (pair - r); int single_b = B - (pair - r); mint x = 1; x *= binom(pair, r); x *= binom(single, single_r); x *= binom(single - single_r + r, single_g); x *= binom(single - single_r + r - single_g, single_b); res += x; } return res; } int solve(int n, int r, int g, int b) { N = n; R = r; G = g; B = b; K = R + G + B; mint ans = 0; for (int pair = 0; pair * 2 <= K; ++pair) { ll single = R + G + B - pair * 2; ans += ::f(single, pair) * ::g(single, pair) * pow2[pair]; } return ans.x; } int main() { pow2[0] = 1; for (int i = 1; i < 3010; ++i) { pow2[i] = pow2[i - 1] * 2; } if (false) { for (int n = 0; n < 30; ++n) { for (int r = 0; r <= 3; ++r) { for (int g = 0; g <= 3; ++g) { for (int b = 0; b <= 3; ++b) { int res = solve(n, r, g, b); int exp = naive(); cout << res << ' ' << exp << endl; assert(res == exp); } } } } } else { int n, r, g, b; cin >> n >> r >> g >> b; cout << solve(n, r, g, b) << endl; } }