/*
 * @Author: qL
 * @Date: 2024-11-06 18:47:17
 * @LastEditTime: 2024-11-07 20:10:10
 * @Problem: Sugar Sweet 3
 * @Link: https://qoj.ac/contest/1780/problem/8942
 * @Solution: Official + Local
 */
#include <cstdio>
#include <algorithm>
#define _(func) __builtin_##func
using i32 = int;
using i64 = long long;
constexpr i32 N = 1000;
constexpr i32 mod = 1e9 + 7;
constexpr i64 qpow(i64 x, i32 p) noexcept {
	i64 r = 1;
	for (; p; p >>= 1, (x *= x) %= mod)
		if (p & 1) (r *= x) %= mod;
	return r;
}
i32 u, v, w, x, pw[N / 2 + 1], n;
i64 fac[N / 2 + 1], ifac[N / 2 + 1];
i64 binom(i32 n, i32 m) noexcept { return n < m || m < 0 ? 0 : fac[n] * ifac[m] % mod * ifac[n - m] % mod; }
i64 Catalan[N / 2 + 1], f[N / 2 + 1][N / 2 + 1], g[N / 2 + 1][N / 2 + 1], h[N / 2 + 1], p[N / 2 + 1], q[N / 2 + 1];
signed main() noexcept {
	scanf("%d%d%d%d", &u, &v, &w, &x), n = (u + v + w);
	if (n & 1) return puts("0"), 0;
	n /= 2;
	fac[0] = 1;
	for (i32 i = 1; i <= n; ++i) fac[i] = fac[i - 1] * i % mod;
	ifac[n] = qpow(fac[n], mod - 2);
	for (i32 i = n; i; --i) ifac[i - 1] = ifac[i] * i % mod;
	for (i32 i = 0; i <= n; ++i) pw[i] = qpow(i, x);
	Catalan[0] = 1;
	for (i32 i = 1; i <= n; ++i)
		for (i32 j = 0; j < i; ++j) (Catalan[i] += Catalan[j] * Catalan[i - j - 1]) %= mod;
	f[0][0] = 1;
	for (i32 i = 1; i <= n; ++i)
		for (i32 j = 1; j <= i; ++j)
			for (i32 k = 0; k < i; ++k) (f[i][j] += f[k][j - 1] * Catalan[i - k - 1]) %= mod;
	for (i32 i = 0; i <= n; ++i)
		for (i32 j = 0; j <= i; ++j) (f[i][j] *= ifac[j]) %= mod;
	for (i32 i = 0; i <= n; ++i)
		for (i32 x = 0; x <= n; ++x) {
			i64 y = 1;
			for (i32 j = 0; j <= i; ++j) (g[i][x] += f[i][j] * y) %= mod, (y *= x) %= mod;
		}
	i64 ans = 0;
	for (i32 a = 0; a <= u; ++a) {
		for (i32 b = 0; b <= v; ++b) {
			i32 c = n - a - b;
			if (c < 0) break;
			i64 now = 0;
			for (i32 i1 = 0; i1 <= v - b; ++i1) {
				i32 i2 = w - c - a + i1, i3 = v - b - i1;
				(now += binom(a, i1) * binom(b, i2) % mod * binom(c, i3)) %= mod;
			}
			for (i32 i = 0; i <= n; ++i) (h[i] += g[a][i] * g[b][i] % mod * g[c][i] % mod * now) %= mod;
		}
	}
	q[0] = 1;
	for (i32 i = 0; i <= n; ++i)
		for (i32 j = i + 1; ~j; --j) q[j] = ((j ? q[j - 1] : 0) + mod - q[j] * i % mod) % mod;
	for (i32 i = 0; i <= n; ++i) {
		i64 t = 1;
		for (i32 j = 0; j <= n; ++j)
			if (i != j) (t *= i - j) %= mod;
		t = h[i] * qpow(t, mod - 2) % mod;
		i64 val = q[n + 1];
		for (i32 j = n; ~j; --j) (p[j] += t * val) %= mod, val = (q[j] + val * i) % mod;
	}
	for (i32 i = 0; i < n; ++i) p[i] < 0 && (p[i] += mod);
	for (i32 i = 0; i <= n; ++i) (ans += p[i] * fac[i] % mod * pw[i]) %= mod;
	printf("%lld\n", (ans + mod) % mod);
	return 0;
}