#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 1000000007;
using Mint = ModInt<MO>;

constexpr int LIM_INV = 100'010;
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];

void prepare() {
  inv[1] = 1;
  for (int i = 2; i < LIM_INV; ++i) {
    inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
  }
  fac[0] = invFac[0] = 1;
  for (int i = 1; i < LIM_INV; ++i) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(Int n, Int k) {
  if (n < 0) {
    if (k >= 0) {
      return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
    } else if (n - k >= 0) {
      return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
    } else {
      return 0;
    }
  } else {
    if (0 <= k && k <= n) {
      assert(n < LIM_INV);
      return fac[n] * invFac[k] * invFac[n - k];
    } else {
      return 0;
    }
  }
}


// [x^n] C^k
Mint catalan(int k, int n) {
  return (k == 0) ? ((n == 0) ? 1 : 0) : (k * fac[2 * n + k - 1] * invFac[n] * invFac[n + k]);
}

// divided differences
vector<Mint> interpolateNewton(const vector<Mint> &xs, const vector<Mint> &ys) {
  const int n = xs.size();
  assert(n == (int)ys.size());
  vector<pair<Mint, Mint>> bs(n);
  for (int i = 0; i < n; ++i) bs[i] = make_pair(ys[i], 1);
  for (int i = 1; i < n; ++i) for (int j = n; --j >= i; ) {
    // (as[j] -= as[j - 1]) /= (xs[j] - xs[j - i]);
    (bs[j].first *= bs[j - 1].second) -= bs[j - 1].first * bs[j].second;
    (bs[j].second *= bs[j - 1].second) *= (xs[j] - xs[j - i]);
  }
  vector<Mint> as(n);
  for (int i = 0; i < n; ++i) as[i] = bs[i].first / bs[i].second;
  return as;
}
// \sum[i] as[i] \prod[0<=j<i] (x - xs[j])
Mint evalNewton(const vector<Mint> &xs, const vector<Mint> &as, Mint x) {
  const int n = xs.size();
  assert(n == (int)as.size());
  Mint y = 0;
  for (int i = n; --i >= 0; ) (y *= (x - xs[i])) += as[i];
  return y;
}


int A, B, C, X;
Mint polys[510][510];

int main() {
  prepare();
  
  for (; ~scanf("%d%d%d%d", &A, &B, &C, &X); ) {
    Mint ans = 0;
    int N = A + B + C;
    if (N % 2 == 0) {
      N /= 2;
      for (int p = 0; p <= N; ++p) {
        for (int t = 0; t <= N; ++t) {
          polys[p][t] = 0;
          for (int i = p; i >= 0; --i) {
            polys[p][t] *= t;
// if(N<=10&&t==0)cerr<<p<<" "<<i<<": "<<catalan(i,p-i)<<endl;
            polys[p][t] += invFac[i] * catalan(i, p - i);
          }
        }
      }
      vector<Mint> xs(N + 1), ys(N + 1, 0);
      for (int x = 0; x <= N; ++x) xs[x] = x;
      for (int p = 0; p <= N; ++p) for (int q = 0; p + q <= N; ++q) {
        const int r = N - p - q;
        Mint way = 0;
        for (int i = 0; i <= p; ++i) {
          const int j = i + (A+B-C)/2 - p;
          const int k = i + B - p - q;
          assert(A == p + j + (r - k));
          assert(B == q + k + (p - i));
          assert(C == r + i + (q - j));
          if (0 <= j && j <= q && 0 <= k && k <= r) {
            way += binom(p, i) * binom(q, j) * binom(r, k);
          }
        }
        if (way) {
// cerr<<p<<" "<<q<<" "<<r<<": "<<way<<endl;
          for (int t = 0; t <= N; ++t) {
            ys[t] += way * polys[p][t] * polys[q][t] * polys[r][t];
          }
        }
      }
      const auto as = interpolateNewton(xs, ys);
      const int n = N + 1;
      vector<Mint> cs(n, 0);
      for (int i = n; --i >= 0; ) {
        for (int j = n - 1 - i; --j >= 0; ) {
          cs[j + 1] += cs[j];
          cs[j] *= -xs[i];
        }
        cs[0] += as[i];
      }
      for (int i = 0; i <= N; ++i) cs[i] *= fac[i];
// cerr<<"cs = "<<cs<<endl;
      for (int i = 0; i <= N; ++i) ans += Mint(i).pow(X) * cs[i];
    }
    printf("%u\n", ans.x);
  }
  return 0;
}