#include <bits/stdc++.h>
using namespace std;
long long n, l, k;
long long a[1000000];
vector<int> vals[5000001];
long long stor[5000000 + 1];
const int MOD = 1000000000 + 7;
inline long long& dp(int i, int j) { return stor[i * n + j]; }
long long func(int i, int j) {
  if (j < 0) return 0;
  if (i == 0) return 0 + max(j + 1, 0);
  if (dp(i, j) != -1) return dp(i, j);
  if (j != 0)
    dp(i, j) = func(i, j - 1);
  else
    dp(i, j) = 0;
  int ni = upper_bound(vals[i - 1].begin(), vals[i - 1].end(), vals[i][j]) -
           vals[i - 1].begin();
  dp(i, j) = (dp(i, j) + func(i - 1, ni - 1)) % MOD;
  return dp(i, j);
}
long long func2(int i, int j) {
  if (j < 0) return 1;
  if (i == 0) return 1 + max(j + 1, 0);
  if (dp(i, j) != -1) return dp(i, j);
  if (j != 0)
    dp(i, j) = func2(i, j - 1);
  else
    dp(i, j) = 1;
  int ni = upper_bound(vals[i - 1].begin(), vals[i - 1].end(), vals[i][j]) -
           vals[i - 1].begin();
  dp(i, j) = (dp(i, j) + func2(i - 1, ni - 1)) % MOD;
  return dp(i, j);
}
int main() {
  std::ios::sync_with_stdio(false);
  memset(stor, -1, sizeof stor);
  cin >> n >> l >> k;
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (long long i = 0; i < l && i < k * n; ++i)
    vals[i / n].push_back(a[i % n]);
  for (int i = 0; i < k; ++i) sort(vals[i].begin(), vals[i].end());
  long long ans = 0;
  for (int i = 0; i < k; ++i) {
    if (vals[i].size() != 0)
      ans = (ans + func(i, vals[i].size() - 1) * ((l / n - i) % MOD)) % MOD;
  }
  if (l % n != 0) {
    memset(stor, -1, sizeof stor);
    for (int i = 0; i < k; ++i) vals[i].clear();
    int v = 0;
    bool add = false;
    for (long long i = max(l / n - k + 1, 0ll) * n; i < l; ++i) {
      add = false;
      vals[v].push_back(a[i % n]);
      if ((i + 1) / n > i / n) {
        ++v;
        add = true;
      }
    }
    if (add) --v;
    for (int i = 0; i <= v; ++i) sort(vals[i].begin(), vals[i].end());
    for (int i = 0; i <= v; ++i) func2(i, vals[i].size() - 1);
    ans = (ans + func2(v, vals[v].size() - 1) + MOD - 1) % MOD;
  }
  cout << ans << endl;
  return 0;
}

### Prompt

In Cpp, your task is to solve 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;
long long n, l, k;
long long a[1000000];
vector<int> vals[5000001];
long long stor[5000000 + 1];
const int MOD = 1000000000 + 7;
inline long long& dp(int i, int j) { return stor[i * n + j]; }
long long func(int i, int j) {
  if (j < 0) return 0;
  if (i == 0) return 0 + max(j + 1, 0);
  if (dp(i, j) != -1) return dp(i, j);
  if (j != 0)
    dp(i, j) = func(i, j - 1);
  else
    dp(i, j) = 0;
  int ni = upper_bound(vals[i - 1].begin(), vals[i - 1].end(), vals[i][j]) -
           vals[i - 1].begin();
  dp(i, j) = (dp(i, j) + func(i - 1, ni - 1)) % MOD;
  return dp(i, j);
}
long long func2(int i, int j) {
  if (j < 0) return 1;
  if (i == 0) return 1 + max(j + 1, 0);
  if (dp(i, j) != -1) return dp(i, j);
  if (j != 0)
    dp(i, j) = func2(i, j - 1);
  else
    dp(i, j) = 1;
  int ni = upper_bound(vals[i - 1].begin(), vals[i - 1].end(), vals[i][j]) -
           vals[i - 1].begin();
  dp(i, j) = (dp(i, j) + func2(i - 1, ni - 1)) % MOD;
  return dp(i, j);
}
int main() {
  std::ios::sync_with_stdio(false);
  memset(stor, -1, sizeof stor);
  cin >> n >> l >> k;
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (long long i = 0; i < l && i < k * n; ++i)
    vals[i / n].push_back(a[i % n]);
  for (int i = 0; i < k; ++i) sort(vals[i].begin(), vals[i].end());
  long long ans = 0;
  for (int i = 0; i < k; ++i) {
    if (vals[i].size() != 0)
      ans = (ans + func(i, vals[i].size() - 1) * ((l / n - i) % MOD)) % MOD;
  }
  if (l % n != 0) {
    memset(stor, -1, sizeof stor);
    for (int i = 0; i < k; ++i) vals[i].clear();
    int v = 0;
    bool add = false;
    for (long long i = max(l / n - k + 1, 0ll) * n; i < l; ++i) {
      add = false;
      vals[v].push_back(a[i % n]);
      if ((i + 1) / n > i / n) {
        ++v;
        add = true;
      }
    }
    if (add) --v;
    for (int i = 0; i <= v; ++i) sort(vals[i].begin(), vals[i].end());
    for (int i = 0; i <= v; ++i) func2(i, vals[i].size() - 1);
    ans = (ans + func2(v, vals[v].size() - 1) + MOD - 1) % MOD;
  }
  cout << ans << endl;
  return 0;
}

```