#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int N = 1005, mod = 1e9 + 7;
int n, A, B, C, x, fac[N], inv[N], ifac[N], f[N][N], g[N][N], h[N], a[N], b[N], ans;
int ksm(int a, int b)
{
	int ret = 1;
	while (b)
	{
		if (b & 1) ret = 1ll * ret * a % mod;
		a = 1ll * a * a % mod; b >>= 1;
	}
	return ret;
}
int c(int n, int m) 
{
    if (n < m || m < 0) return 0;
    return 1ll * fac[n] * ifac[m] % mod * ifac[n-m] % mod;
}
void add(int &x, int y) {if ((x += y) >= mod) x -= mod;}
int main()
{
    fac[0] = inv[0] = inv[1] = ifac[0] = 1;
    for (int i = 1; i < N; i++) fac[i] = 1ll * fac[i-1] * i % mod;
    for (int i = 2; i < N; i++) inv[i] = 1ll * inv[mod%i] * (mod - mod / i) % mod;
    for (int i = 1; i < N; i++) ifac[i] = 1ll * ifac[i-1] * inv[i] % mod;
    cin >> A >> B >> C >> x;
    if (A + B + C & 1) return cout << 0, 0; 
    n = (A + B + C) / 2; f[0][0] = 1;
    for (int i = 1; i <= n; i++) f[1][i] = 1ll * c(2 * i - 2, i - 1) * inv[i] % mod;
    for (int i = 2; i <= n; i++) for (int j = i - 1; j <= n; j++) 
        for (int k = 1; k <= n - j; k++) add(f[i][j+k], 1ll * f[i-1][j] * f[1][k] % mod);
    for (int i = 0; i <= n; i++) for (int j = 0; j <= n; j++) 
        f[i][j] = 1ll * f[i][j] * ifac[i] % mod;
    for (int i = 0; i <= n; i++) for (int j = 0; j <= n; j++) 
        for (int k = n; k >= 0; k--) g[i][j] = (1ll * g[i][j] * j + f[k][i]) % mod;
    for (int i = 0; i <= A; i++) for (int j = 0; j <= B; j++)
    {
        int k = n - i - j, mul = 0;
        if (k < 0 || k > C) continue;
        for (int o = 0; o <= C - k; o++)
        {
            int v = o - i - j + B, u = v - k - i + A;
			if (u < 0 || u > A - i) continue;
			if (v < 0 || v > B - j) continue;
			add(mul, 1ll * c(i, o) * c(j, u) % mod * c(k, v) % mod);
        }
        for (int o = 0; o <= n; o++) 
            add(h[o], 1ll * g[i][o] * g[j][o] % mod * g[k][o] % mod * mul % mod);
    }
    for (int i = 0; i <= n; i++)
	{
		h[i] = 1ll * h[i] * ifac[i] % mod * ifac[n-i] % mod;
		if ((n ^ i) & 1) h[i] = mod - h[i];
	}
	b[0] = 1;
	for (int i = 0; i <= n; i++) for (int j = i + 1; j >= 0; j--)
		a[j] = ((j ? a[j-1] : 0) + 1ll * (mod - i) * a[j] + 1ll * h[i] * b[j]) % mod,
		b[j] = ((j ? b[j-1] : 0) + 1ll * (mod - i) * b[j]) % mod;
	for (int i = 0; i <= n; i++) ans = (ans + 1ll * a[i] * fac[i] % mod * ksm(i, x)) % mod;
    cout << ans << "\n";
    return 0; 
}