#include <bits/stdc++.h>
#include <iostream>
#include <set>
#include <string>
#include <map>
using namespace std;
const int MOD = 1e9 + 7;

int power(int x, int t) {
    int ret = 1;
    while(t > 0) {
        if(t & 1) ret = 1LL * ret * x % MOD;
        x = 1LL * x * x % MOD;
        t >>= 1;
    }
    return ret;
}
int n, comb[1005][1005];
int px[505][505], pv[505][505], cat[505], tmp[505], ifac[505], fac[505], inv[505];

void init() {
    comb[0][0] = 1;
    for(int i = 1; i <= 2 * n; i++) {
        comb[i][0] = 1;
        for(int j = 1; j <= i; j++) comb[i][j] = (comb[i - 1][j - 1] + comb[i - 1][j]) % MOD;
    }

    fac[0] = 1;
    for(int i = 1; i <= n; i++) fac[i] = 1LL * fac[i - 1] * i % MOD;
    ifac[n] = power(fac[n], MOD - 2);
    for(int i = n; i >= 1; i--) ifac[i - 1] = 1LL * ifac[i] * i % MOD;
    for(int i = 1; i <= n; i++) inv[i] = 1LL * ifac[i] * fac[i - 1] % MOD;
    
    for(int i = 1; i <= n; i++) cat[i] = 1LL * inv[i] * comb[2 * i - 2][i - 1] % MOD;

    tmp[0] = 1;
    px[0][0] = 1;
    for(int i = 1; i <= n; i++) {
        for(int j = n; j >= i; j--) {
            tmp[j] = 0;
            for(int k = i - 1; k < j; k++) tmp[j] = (tmp[j] + 1LL * tmp[k] * cat[j - k]) % MOD;
            px[j][i] = 1LL * tmp[j] * ifac[i] % MOD;
        }
    }

    for(int i = 0; i <= n; i++) for(int j = 0; j <= n; j++) {
        pv[i][j] = 0;
        for(int k = i; k >= 0; k--) pv[i][j] = (1LL * pv[i][j] * j + px[i][k]) % MOD;
    }
}

int a, b, c, x, y, z, t, pc[505][505], av[505], ax[505];

void pmul(int n1, int n2, int n3, int coef) {
    for(int i = 0; i <= n; i++) av[i] = (av[i] + 1LL * pv[n1][i] * pv[n2][i] % MOD * pv[n3][i] % MOD * coef) % MOD;
}

vector<int> interpolate(vector<int> x, vector<int> y, int n) {
    vector<int> res(n), temp(n);
    for(int k = 0; k < n - 1; k++) for(int i = k + 1; i < n; i++)
        y[i] = 1LL * (y[i] - y[k] + MOD) * power((x[i] - x[k] + MOD) % MOD, MOD - 2) % MOD;
    int last = 0; temp[0] = 1;
    for(int k = 0; k < n; k++) for(int i = 0; i < n; i++) {
        res[i] = (res[i] + 1LL * y[k] * temp[i]) % MOD;
        swap(last, temp[i]);
        temp[i] = (temp[i] + 1LL * (MOD - last) * x[k]) % MOD;
    }
    return res;
}

void calc() {
    vector<int> x, y, z;
    for(int i = 0; i <= n; i++) {
        x.push_back(i); y.push_back(av[i]);
    }
    z = interpolate(x, y, n + 1);
    for(int i = 0; i <= n; i++) ax[i] = z[i];
}

int main() {;
    scanf("%d%d%d%d", &a, &b, &c, &t);
    n = a + b + c;
    if(n & 1) {
        printf("0\n"); return 0;
    }
    n /= 2;
    a = n - a; b = n - b; c = n - c;
    if(a < 0 || b < 0 || c < 0) {
        printf("0\n"); return 0;
    }

    init();
    for(int i = 0; i <= a; i++) for(int j = 0; j <= b; j++) for(int k = 0; k <= c; k++) {
        int ci = i + b - j, cj = j + c - k, ck = k + a - i;
        pc[ci][cj] = (pc[ci][cj] + 1LL * comb[ci][i] * comb[cj][j] % MOD * comb[ck][k]) % MOD;
    }
    for(int i = 0; i <= n; i++) for(int j = 0; i + j <= n; j++) {
        int k = n - i - j;
        pmul(i, j, k, pc[i][j]);
    }
    calc();

    int ans = 0;
    for(int i = 0; i <= n; i++) ans = (ans + 1LL * ax[i] * fac[i] % MOD * power(i, t)) % MOD;
    printf("%d\n", ans);
    return 0;
}