#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T, class U>
void chmin(T& t, const U& u) {
  if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
  if (t < u) t = u;
}
template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
  os << "(" << p.first << "," << p.second << ")";
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
  os << "{";
  for (int i = 0; i < (v.size()); i++) {
    if (i) os << ",";
    os << v[i];
  }
  os << "}";
  return os;
}
template <unsigned int MOD>
struct ModInt {
  using uint = unsigned int;
  using ull = unsigned long long;
  using M = ModInt;
  uint v;
  ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
  M& set_norm(uint _v) {
    v = (_v < MOD) ? _v : _v - MOD;
    return *this;
  }
  explicit operator bool() const { return v != 0; }
  M operator+(const M& a) const { return M().set_norm(v + a.v); }
  M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
  M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
  M operator/(const M& a) const { return *this * a.inv(); }
  M& operator+=(const M& a) { return *this = *this + a; }
  M& operator-=(const M& a) { return *this = *this - a; }
  M& operator*=(const M& a) { return *this = *this * a; }
  M& operator/=(const M& a) { return *this = *this / a; }
  M operator-() const { return M() - *this; }
  M& operator++(int) { return *this = *this + 1; }
  M& operator--(int) { return *this = *this - 1; }
  M pow(ll n) const {
    if (n < 0) return inv().pow(-n);
    M x = *this, res = 1;
    while (n) {
      if (n & 1) res *= x;
      x *= x;
      n >>= 1;
    }
    return res;
  }
  M inv() const {
    ll a = v, b = MOD, p = 1, q = 0, t;
    while (b != 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(p -= t * q, q);
    }
    return M(p);
  }
  bool operator==(const M& a) const { return v == a.v; }
  bool operator!=(const M& a) const { return v != a.v; }
  friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
  static uint get_mod() { return MOD; }
};
using Mint = ModInt<1000000007>;
const int maxv = 1000010;
V<Mint> fact(maxv), ifact(maxv), inv(maxv);
void init() {
  fact[0] = 1;
  for (int i = 1; i < maxv; ++i) {
    fact[i] = fact[i - 1] * i;
  }
  ifact[maxv - 1] = fact[maxv - 1].inv();
  for (int i = maxv - 2; i >= 0; --i) {
    ifact[i] = ifact[i + 1] * (i + 1);
  }
  for (int i = 1; i < maxv; ++i) {
    inv[i] = ifact[i] * fact[i - 1];
  }
}
Mint comb(int n, int r) {
  if (n < 0 || r < 0 || r > n) return Mint(0);
  return fact[n] * ifact[r] * ifact[n - r];
}
const int maxk = 2010;
Mint dp[24][maxk];
int main() {
  init();
  int n, m, k, s;
  cin >> n >> m >> k >> s;
  V<pii> vec(k);
  for (int i = 0; i < (k); i++) {
    int r, c;
    cin >> r >> c;
    --r, --c;
    vec[i] = make_pair(r, c);
  }
  vec.emplace_back(0, 0);
  vec.emplace_back(n - 1, m - 1);
  sort((vec).begin(), (vec).end());
  k = vec.size();
  for (int i = 0; i < (k); i++) {
    int r, c;
    tie(r, c) = vec[i];
    for (int j = 0; j < (24); j++) {
      dp[j][i] = comb(r + c, r);
      for (int p = 0; p < (i); p++) {
        int nr, nc;
        tie(nr, nc) = vec[p];
        if (nc <= c) {
          Mint dec = dp[j][p];
          if (j) dec -= dp[j - 1][p];
          dp[j][i] -= dec * comb(r - nr + c - nc, r - nr);
        }
      }
    }
  }
  Mint all = comb(n - 1 + m - 1, n - 1);
  Mint ans = (all - dp[23][k - 1]);
  for (int j = 0; j < (23); j++) {
    ans += (dp[j + 1][k - 1] - dp[j][k - 1]) * s;
    s = (s + 1) / 2;
  }
  ans /= all;
  cout << ans << endl;
  return 0;
}
