Problem: There used to be unrest in the Galactic Senate. Several thousand solar systems had declared their intentions to leave the Republic. But fear not! Master Heidi was able to successfully select the Jedi Knights that have restored peace in the galaxy. However, she knows that evil never sleeps and a time may come when she will need to pick another group of Jedi Knights. She wants to be sure she has enough options to do so.

There are n Jedi Knights, each of them with a lightsaber of one of m colors. Given a number k, compute the number of differently colored collections of k lightsabers that some k Jedi Knights might have. Jedi Knights with lightsabers of the same color are indistinguishable (it's not the person, it's the lightsaber color that matters!), and their order does not matter; that is, we consider two collections of Jedi Knights to be different if and only if their vectors of counts of lightsabers of each color (like what you were given in the easy and the medium versions) are different. We count all subsets, not only contiguous subsegments of the input sequence. Output the answer modulo 1009.

Input

The first line of the input contains n (1 ≤ n ≤ 2·105), m (1 ≤ m ≤ n) and k (1 ≤ k ≤ n). The second line contains n integers in the range {1, 2, ..., m} representing colors of the lightsabers of subsequent Jedi Knights.

Output

Output one number: the number of differently colored collections of k lightsabers modulo 1009.

Example

Input

4 3 2
1 2 3 2


Output

4

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename dbl>
struct cplx {
  dbl x, y;
  cplx(dbl x_ = 0, dbl y_ = 0) : x(x_), y(y_) {}
  friend cplx operator+(cplx a, cplx b) { return cplx(a.x + b.x, a.y + b.y); }
  friend cplx operator-(cplx a, cplx b) { return cplx(a.x - b.x, a.y - b.y); }
  friend cplx operator*(cplx a, cplx b) {
    return cplx(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);
  }
  friend cplx conj(cplx a) { return cplx(a.x, -a.y); }
  friend cplx inv(cplx a) {
    dbl n = (a.x * a.x + a.y * a.y);
    return cplx(a.x / n, -a.y / n);
  }
};
string to_string(string s) { return '"' + s + '"'; }
string to_string(const char* ch) { return string(ch); }
string to_string(char ch) { return (string) "'" + ch + (string) "'"; }
string to_string(bool b) { return (b ? "true" : "false"); }
template <class A, class B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
string to_string(complex<double> a) {
  return "(" + to_string(real(a)) + ", " + to_string(imag(a)) + ")";
}
string to_string(vector<complex<double>> a) {
  string res = "{";
  bool first = true;
  int n = a.size();
  for (int i = 0; i < n; i++) {
    auto x = a[i];
    if (first == false) res += ", ";
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
string to_string(cplx<double> a) {
  return "(" + to_string((a.x)) + ", " + to_string((a.y)) + ")";
}
string to_string(vector<cplx<double>> a) {
  string res = "{";
  bool first = true;
  int n = a.size();
  for (int i = 0; i < n; i++) {
    auto x = a[i];
    if (first == false) res += ", ";
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <class A>
string to_string(A a) {
  string res = "{";
  bool first = true;
  for (const auto& x : a) {
    if (first == false) res += ", ";
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug() { cerr << "]\n"; }
template <class H, class... T>
void debug(H head, T... tail) {
  cerr << to_string(head) << " ";
  debug(tail...);
}
using cd = cplx<double>;
const double PI = acos(-1);
class FFT {
 public:
  static int base;
  static vector<int> rev;
  static vector<cd> roots;
  static void init() {
    rev = {0, 1};
    roots = vector<cd>(2, 1);
    base = 1;
  }
  static void ensure_base(int new_base) {
    if (roots.empty() || rev.empty()) {
      init();
    }
    if (base >= new_base) {
      return;
    }
    rev.resize(1 << new_base);
    for (int i = 0; i < (1 << new_base); i++) {
      rev[i] = ((rev[i / 2] >> 1) | (i % 2) << (new_base - 1));
    }
    roots.resize(1 << new_base);
    while (base < new_base) {
      const auto z1 = polar(1.0, PI / (1 << base));
      const auto z = cd(real(z1), imag(z1));
      for (int i = (1 << (base - 1)); i < (1 << base); i++) {
        roots[i << 1] = roots[i];
        roots[(i << 1) + 1] = roots[i] * z;
      }
      base++;
    }
  }
  static void fft(vector<cd>& a) {
    int n = a.size();
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for (int i = 0; i < n; i++) {
      if (i < (rev[i] >> shift)) swap(a[i], a[rev[i] >> shift]);
    }
    for (int k = 1; k < n; k *= 2) {
      for (int i = 0; i < n; i += 2 * k) {
        for (int j = 0; j < k; j++) {
          auto x = a[i + j], y = a[i + j + k] * roots[k + j];
          a[i + j] = x + y;
          a[i + j + k] = x - y;
        }
      }
    }
  }
  template <typename T>
  static vector<T> multiply(vector<T> a, vector<T> b) {
    if (a.empty() || b.empty()) return {};
    int total = int(a.size() + b.size()) - 1;
    int n = 1 << (32 - __builtin_clz(total));
    ;
    vector<cd> A(n), B(n);
    for (int i = 0; i < n; i++) {
      T x = (i < int(a.size()) ? a[i] : 0);
      T y = (i < int(b.size()) ? b[i] : 0);
      A[i] = cd(x, y);
    }
    fft(A);
    for (auto& i : A) {
      i = i * i;
    }
    for (int i = 0; i < n; i++) {
      B[i] = A[(n - i) & (n - 1)] - conj(A[i]);
    }
    fft(B);
    ;
    vector<T> res(total);
    for (int i = 0; i < total; i++) {
      res[i] = (llround(B[i].y)) / (4 * n);
    }
    return res;
  }
  template <typename T, typename Z = int64_t>
  static vector<T> multiply_mod(vector<T> a, vector<T> b, Z m) {
    if (a.empty() || b.empty()) return {};
    int total = int(a.size() + b.size()) - 1;
    int n = 1 << (32 - __builtin_clz(total));
    vector<cd> A(n), B(n);
    const int shift = 15;
    for (int i = 0; i < int(a.size()); i++) {
      assert(a[i] >= 0 && a[i] < m);
      T x = (a[i] % m + m) % m;
      A[i] = cd(x & ((1 << shift) - 1), x >> shift);
    }
    fft(A);
    if (a == b)
      B = A;
    else {
      for (int i = 0; i < int(b.size()); i++) {
        assert(b[i] >= 0 && b[i] < m);
        T x = (b[i] % m + m) % m;
        B[i] = cd(x & ((1 << shift) - 1), x >> shift);
      }
      fft(B);
    }
    double ratio = 0.25 / n;
    cd r2(0, -1);
    cd r3(ratio, 0);
    cd r4(0, -ratio);
    cd r5(0, 1);
    for (int i = 0; i <= (n >> 1); i++) {
      int j = (n - i) & (n - 1);
      cd a1 = (A[i] + conj(A[j]));
      cd a2 = (A[i] - conj(A[j])) * r2;
      cd b1 = (B[i] + conj(B[j])) * r3;
      cd b2 = (B[i] - conj(B[j])) * r4;
      if (i != j) {
        cd c1 = (A[j] + conj(A[i]));
        cd c2 = (A[j] - conj(A[i])) * r2;
        cd d1 = (B[j] + conj(B[i])) * r3;
        cd d2 = (B[j] - conj(B[i])) * r4;
        A[i] = c1 * d1 + c2 * d2 * r5;
        B[i] = c1 * d2 + c2 * d1;
      }
      A[j] = a1 * b1 + a2 * b2 * r5;
      B[j] = a1 * b2 + a2 * b1;
    }
    fft(A);
    fft(B);
    vector<T> res(total);
    for (int i = 0; i < total; i++) {
      Z aa = llround(A[i].x);
      Z bb = llround(B[i].x);
      Z cc = llround(A[i].y);
      res[i] = static_cast<T>((aa + ((bb % m) << 15) + ((cc % m) << 30)) % m);
      if (res[i] < 0 || res[i] >= m) {
        ;
      }
      assert(res[i] >= 0 && res[i] < m);
    }
    return res;
  }
};
int FFT::base;
vector<int> FFT::rev;
vector<cd> FFT::roots;
template <typename T>
vector<T> operator*(const vector<T>& A, const vector<T>& B) {
  if (min((int)A.size(), (int)B.size()) < 0) {
    vector<T> C((int)A.size() + (int)B.size() - 1);
    for (int i = 0; i < (int)A.size(); i++) {
      for (int j = 0; j < (int)B.size(); j++) {
        C[i + j] += A[i] * B[j];
      }
    }
    return C;
  }
  return FFT::multiply<T>(A, B);
}
template <typename T>
vector<T> operator*=(vector<T>& A, const vector<T>& B) {
  return A = A * B;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n, m, k;
  cin >> n >> m >> k;
  map<int, int> mp;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    mp[x]++;
  }
  vector<pair<int, vector<int64_t>>> a;
  for (auto& i : mp) {
    a.push_back(make_pair(i.second, vector<int64_t>(i.second + 1, 1)));
  }
  while (a.size() > 1) {
    sort(a.begin(), a.end());
    for (auto& i : a) {
      ;
    }
    vector<pair<int, vector<int64_t>>> b;
    for (int i = 0; i + 1 < int(a.size()); i += 2) {
      auto xx = FFT::multiply_mod<int64_t, int64_t>(a[i].second,
                                                    a[i + 1].second, 1009);
      ;
      b.push_back(make_pair(xx.size(), xx));
    }
    if (int(a.size()) % 2 == 1) b.push_back(a.back());
    a = b;
  }
  assert(int(a.size()) == 1);
  cout << a.front().second[k] << '\n';
  return 0;
}