#include <bits/stdc++.h>
using namespace std;
vector<vector<long long> > dp[3];
const int mod = 1000000007;
vector<pair<int, int> > arr;
struct element {
 private:
  int value;
  int position;
  int sz;
  int v;

 public:
  element(int value, int position) {
    this->value = value;
    this->position = position;
    sz = 1;
    v = 0;
  }
  void inc() { sz++; }
  void incvalid() { v++; }
  int size() { return sz; }
  int valid() { return v; }
  void print() {
    cout << value << " " << position << " " << sz << " valid:" << v << endl;
  }
};
vector<element> inf;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n, k, l;
  cin >> n >> l >> k;
  int a;
  for (int i = 0; i < n; i++) {
    cin >> a;
    arr.push_back(pair<int, int>(a, i));
  }
  sort(arr.begin(), arr.end());
  inf.push_back(element(arr[0].first, 0));
  if (arr[0].second < l % n) inf[0].incvalid();
  for (int i = 1; i < n; i++) {
    if (arr[i].first == arr[i - 1].first)
      inf.back().inc();
    else
      inf.push_back(element(arr[i].first, i));
    if (arr[i].second < l % n) inf.back().incvalid();
  }
  for (int i = 0; i < 2; i++) {
    dp[i].resize(inf.size() + 2);
    for (int j = 0; j <= inf.size() + 1; j++) dp[i][j].resize(k + 2);
  }
  long long seq = l / n;
  for (int i = 0; i < inf.size(); i++) dp[0][i][0] = 1;
  for (int i = 0; i < inf.size(); i++)
    if (inf[i].valid()) dp[1][i][0] = 1;
  for (int tk = 1; tk <= k; tk++) {
    for (int ind = inf.size() - 1; ind >= 0; ind--) {
      dp[0][ind][tk] =
          (dp[0][ind + 1][tk] + dp[0][ind][tk - 1] * inf[ind].size()) % mod;
      dp[1][ind][tk] = (dp[1][ind + 1][tk] +
                        dp[1][ind][tk - 1] * inf[ind].size() * (tk > 1) +
                        dp[1][ind][tk - 1] * inf[ind].valid() * (tk == 1)) %
                       mod;
    }
  }
  long long res = 0, md_seq = seq % mod;
  ;
  for (int i = 1; i <= min(seq, k); i++)
    res = (res + dp[0][0][i] * (md_seq - i + 1 + mod)) % mod;
  if (l % n)
    for (int i = 1; i <= min(seq + 1, k); i++) res = (res + dp[1][0][i]) % mod;
  cout << res << "\n";
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

While Duff was resting in the beach, she accidentally found a strange array b0, b1, ..., bl - 1 consisting of l positive integers. This array was strange because it was extremely long, but there was another (maybe shorter) array, a0, ..., an - 1 that b can be build from a with formula: bi = ai mod n where a mod b denoted the remainder of dividing a by b.

<image>

Duff is so curious, she wants to know the number of subsequences of b like bi1, bi2, ..., bix (0 ≤ i1 < i2 < ... < ix < l), such that: 

  * 1 ≤ x ≤ k
  * For each 1 ≤ j ≤ x - 1, <image>
  * For each 1 ≤ j ≤ x - 1, bij ≤ bij + 1. i.e this subsequence is non-decreasing. 



Since this number can be very large, she want to know it modulo 109 + 7.

Duff is not a programmer, and Malek is unavailable at the moment. So she asked for your help. Please tell her this number.

Input

The first line of input contains three integers, n, l and k (1 ≤ n, k, n × k ≤ 106 and 1 ≤ l ≤ 1018).

The second line contains n space separated integers, a0, a1, ..., an - 1 (1 ≤ ai ≤ 109 for each 0 ≤ i ≤ n - 1). 

Output

Print the answer modulo 1 000 000 007 in one line.

Examples

Input

3 5 3
5 9 1


Output

10


Input

5 10 3
1 2 3 4 5


Output

25

Note

In the first sample case, <image>. So all such sequences are: <image>, <image>, <image>, <image>, <image>, <image>, <image>, <image>, <image> and <image>.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
vector<vector<long long> > dp[3];
const int mod = 1000000007;
vector<pair<int, int> > arr;
struct element {
 private:
  int value;
  int position;
  int sz;
  int v;

 public:
  element(int value, int position) {
    this->value = value;
    this->position = position;
    sz = 1;
    v = 0;
  }
  void inc() { sz++; }
  void incvalid() { v++; }
  int size() { return sz; }
  int valid() { return v; }
  void print() {
    cout << value << " " << position << " " << sz << " valid:" << v << endl;
  }
};
vector<element> inf;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n, k, l;
  cin >> n >> l >> k;
  int a;
  for (int i = 0; i < n; i++) {
    cin >> a;
    arr.push_back(pair<int, int>(a, i));
  }
  sort(arr.begin(), arr.end());
  inf.push_back(element(arr[0].first, 0));
  if (arr[0].second < l % n) inf[0].incvalid();
  for (int i = 1; i < n; i++) {
    if (arr[i].first == arr[i - 1].first)
      inf.back().inc();
    else
      inf.push_back(element(arr[i].first, i));
    if (arr[i].second < l % n) inf.back().incvalid();
  }
  for (int i = 0; i < 2; i++) {
    dp[i].resize(inf.size() + 2);
    for (int j = 0; j <= inf.size() + 1; j++) dp[i][j].resize(k + 2);
  }
  long long seq = l / n;
  for (int i = 0; i < inf.size(); i++) dp[0][i][0] = 1;
  for (int i = 0; i < inf.size(); i++)
    if (inf[i].valid()) dp[1][i][0] = 1;
  for (int tk = 1; tk <= k; tk++) {
    for (int ind = inf.size() - 1; ind >= 0; ind--) {
      dp[0][ind][tk] =
          (dp[0][ind + 1][tk] + dp[0][ind][tk - 1] * inf[ind].size()) % mod;
      dp[1][ind][tk] = (dp[1][ind + 1][tk] +
                        dp[1][ind][tk - 1] * inf[ind].size() * (tk > 1) +
                        dp[1][ind][tk - 1] * inf[ind].valid() * (tk == 1)) %
                       mod;
    }
  }
  long long res = 0, md_seq = seq % mod;
  ;
  for (int i = 1; i <= min(seq, k); i++)
    res = (res + dp[0][0][i] * (md_seq - i + 1 + mod)) % mod;
  if (l % n)
    for (int i = 1; i <= min(seq + 1, k); i++) res = (res + dp[1][0][i]) % mod;
  cout << res << "\n";
}

```