#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef vector<ll> poly;

const ll mo=1e9+7;

ll n;
ll f[505][505], g[505][505], ans[505], ans2[505];
ll V[505], fac[1005], ifac[1005];

ll C(ll n,ll m) {
    if(n<m||n<0||m<0) return 0;
    return fac[n]*ifac[m]%mo*ifac[n-m]%mo;
}

ll qpow(ll a,ll p) {
    ll res=1;
    while(p) {
        if(p&1) res=res*a%mo;
        p>>=1, a=a*a%mo;
    }
    return res;
}

poly mul(poly a,poly b) {
    poly c(a.size()+b.size()-1,0);
    for(ll i=0;i<a.size();i++) {
        for(ll j=0;j<b.size();j++) {
            (c[i+j]+= a[i]*b[j]%mo)%=mo;
        }
    }
    return c;
}

poly div(poly a,ll c) {
    poly b(a.size()-1,0);
    for(ll i=b.size()-1;i>=0;i--) {
        b[i]=a[i+1];
        (a[i]+= c*b[i]%mo)%=mo;
    }
    return b;
}

void lglr() {
    poly t={1};
    for(ll i=0;i<=n/2;i++) t=mul(t,poly{(mo-i)%mo,1});
    for(ll i=0;i<=n/2;i++) {
        poly t2=div(t,i);
        ll coef=ifac[i]%mo*ifac[n/2-i]%mo*((n/2-i)&1?mo-1:1)%mo;
        for(ll j=0;j<=n/2;j++) (ans2[j]+= coef*ans[i]%mo*t2[j]%mo)%=mo;
    }
    return ;
}

int main() {
    // freopen("game.in","r",stdin);
    // freopen("game.out","w",stdout);
    ios::sync_with_stdio(false);
    cin.tie(0), cout.tie(0);
    ll u,v,w,x; cin>>u>>v>>w>>x;
    n=u+v+w;
    if(n&1) {
        cout<<"0\n";
        return 0;
    }
    fac[0]=1;
    for(ll i=1;i<=n;i++) fac[i]=fac[i-1]*i%mo;
    ifac[n]=qpow(fac[n],mo-2);
    for(ll i=n-1;i>=0;i--) ifac[i]=ifac[i+1]*(i+1)%mo;
    for(ll i=1;i<=n/2;i++) V[i]=(C(i*2-2,i-1)-C(i*2-2,i-2)+mo)%mo;
    f[0][0]=1;
    for(ll i=1;i<=n/2;i++) {
        for(ll j=i;j<=n/2;j++) {
            for(ll k=1;k<=j;k++) {
                (f[j][i]+= f[j-k][i-1]*V[k]%mo)%=mo;
            }
        }
    }
    for(ll i=0;i<=n/2;i++) {
        for(ll j=0;j<=n/2;j++) (f[i][j]*= ifac[j])%=mo;
        for(ll v=0;v<=n/2;v++) {
            for(ll j=0,pw=1;j<=n/2;j++,pw=pw*v%mo) (g[i][v]+= pw*f[i][j]%mo)%=mo;
        }
    }
    for(ll x=0;x<=n/2;x++) {
        for(ll y=0;x+y<=n/2;y++) {
            ll coef=0;
            ll z=n/2-x-y;
            for(ll a=0;a<=x;a++) {
                ll c=y+z+a-v;
                ll b=x+y+z-a-w;
                (coef+= C(x,a)*C(y,b)%mo*C(z,c)%mo)%=mo;
            }
            if(!coef) continue;
            for(ll i=0;i<=n/2;i++) (ans[i]+= g[x][i]*g[y][i]%mo*g[z][i]%mo*coef%mo)%=mo;
        }
    }
    lglr();
    ll sum=0;
    for(ll i=1;i<=n/2;i++) (sum+= qpow(i,x)*ans2[i]%mo*fac[i]%mo)%=mo;
    cout<<sum<<'\n';
    return 0;
}