#include <bits/stdc++.h>
using namespace std;
int read() {
    int x = 0, f = 1; char c = getchar();
    while (c < '0' || c > '9') {if (c == '-') f = -f; c = getchar();}
    while (c >= '0' && c <= '9') {x = x * 10 + (c ^ 48); c = getchar();}
    return x * f;
}
int quickpow(int a, int b, int mod) {
    int res = 1;
    for (; b; b >>= 1, a = 1LL * a * a % mod)
        if (b & 1) res = 1LL * res * a % mod;
    return res;
}
const int N = 1005, mod = 1e9 + 7;
int a, b, c, x, m, n, ans;
int f[N][N], fac[N], Inv[N], inv[N], F[N][N], G[N], g[N], h[N];
void mul(int *f, int c) {
    for (int i = 0; i <= m; i++) f[i] = 1LL * f[i] * c % mod;
}
void mull(int *f, int p) {
    for (int i = m + 1; ~i; i--) {
        f[i] = 1LL * f[i] * p % mod;
        if (i) f[i] = (f[i] + f[i - 1]) % mod;
    }
}
void divv(int *f, int p) {
    for (int i = 0; i <= m + 1; i++) {
        if (i) f[i] = (f[i] - f[i - 1] + mod) % mod;
        f[i] = 1LL * f[i] * p % mod;
    }
}
int C(int a, int b) {
    if (a < 0 || b < 0 || a < b) return 0;
    return 1LL * fac[a] * Inv[b] % mod * Inv[a - b] % mod;
}
void add(int &x, int y) {
    x += y;
    if (x >= mod) x -= mod;
}
void Solve() {
    a = read(); b = read(); c = read(); x = read(); n = a + b + c;
    if (n & 1) return void(puts("0")); m = n >> 1;
    fac[0] = 1;
    for (int i = 1; i <= n; i++) fac[i] = 1LL * fac[i - 1] * i % mod;
    Inv[n] = quickpow(fac[n], mod - 2, mod);
    for (int i = n - 1; ~i; i--) Inv[i] = 1LL * Inv[i + 1] * (i + 1) % mod;
    for (int i = 1; i <= n; i++) inv[i] = 1LL * Inv[i] * fac[i - 1] % mod;
    f[0][0] = 1;
    for (int i = 1; i <= m; i++)
        for (int j = 1; j <= m; j++)
            for (int k = 0; k < i; k++)
                f[i][j] = (f[i][j] + 1LL * f[i - k - 1][j - 1] * (C(k * 2, k) - C(k * 2, k + 1) + mod)) % mod;
    for (int u = 0; u <= m; u++)
        for (int x = 0; x <= m; x++) {
            int s = 1;
            for (int i = 0; i <= m; i++) {
                F[u][x] = (F[u][x] + 1LL * f[u][i] * s % mod * Inv[i]) % mod;
                s = 1LL * s * x % mod;
            }
        }
    for (int u = 0; u <= min(a, m); u++)
        for (int v = 0; v <= b && u + v <= m; v++) {
            int w = m - u - v, res = 0;
            for (int xb = 0; xb <= a - u; xb++) {
                int xc = a - u - xb, zb = v - xb, za = c - w - zb, ya = u - za, yc = b - v - ya;
                if (xb < 0 || xc < 0 || ya < 0 || yc < 0 || za < 0 || zb < 0) continue;
                res = (res + 1LL * C(u, ya) * C(v, zb) % mod * C(w, xc)) % mod;
            }
            for (int i = 0; i <= m; i++) G[i] = (G[i] + 1LL * F[u][i] * F[v][i] % mod * F[w][i] % mod * res) % mod;
        }
    h[0] = 1;
    for (int i = 1; i <= m; i++) mull(h, (mod - i) % mod);
    for (int i = 0; i <= m; i++) {
        if (i) divv(h, (mod - inv[i]) % mod);
        int t = 1LL * Inv[i] * Inv[m - i] % mod * G[i] % mod;
        if ((m - i) & 1) t = (mod - t) % mod;
        for (int j = 0; j <= m; j++) g[j] = (g[j] + 1LL * h[j] * t) % mod;
        mull(h, (mod - i) % mod);
    }
    for (int i = 0; i <= m; i++) ans = (ans + 1LL * g[i] * quickpow(i, x, mod) % mod * fac[i]) % mod;
    printf("%d\n", ans);
}
int main() {
    int _ = 1;
    while (_--) Solve();
    return 0;
}