#include <bits/stdc++.h>
const int N = 1e6 + 7, mod = 1e9 + 7;
std::vector<std::pair<int, int>> input;
int tab[N];
long long countEnd[N];
long long count[N];
long long _dp[2][N];
int main() {
  long long *dp = _dp[1];
  long long *prev = _dp[0];
  long long n, k, l;
  scanf("%lld%lld%lld", &n, &l, &k);
  int x;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &x);
    input.push_back({x, i});
  }
  std::sort(input.begin(), input.end());
  long long maxdl = std::min(k, (l + n - 1) / n);
  long long koncowka = l % n;
  if (koncowka == 0) koncowka = n;
  int last = -2, nr = 0;
  for (auto it : input) {
    if (it.first != last) {
      last = it.first;
      nr++;
    }
    count[nr]++;
    if (it.second <= koncowka) {
      countEnd[nr]++;
    }
    tab[it.second] = nr;
  }
  long long wyn = 0;
  long long ileKawalkow = (l - 1) / n;
  for (int i = 1; i <= nr; i++) prev[i] = 1;
  for (int dl = 1; dl <= maxdl; dl++) {
    for (int num = 1; num <= nr; num++) {
      dp[num] = prev[num];
      wyn += (((count[num] * (ileKawalkow - dl + 1) + countEnd[num])) % mod) *
             dp[num];
      wyn %= mod;
      dp[num] *= count[num];
      dp[num] += dp[num - 1];
      dp[num] %= mod;
    }
    std::swap(dp, prev);
  }
  printf("%lld", wyn);
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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>
const int N = 1e6 + 7, mod = 1e9 + 7;
std::vector<std::pair<int, int>> input;
int tab[N];
long long countEnd[N];
long long count[N];
long long _dp[2][N];
int main() {
  long long *dp = _dp[1];
  long long *prev = _dp[0];
  long long n, k, l;
  scanf("%lld%lld%lld", &n, &l, &k);
  int x;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &x);
    input.push_back({x, i});
  }
  std::sort(input.begin(), input.end());
  long long maxdl = std::min(k, (l + n - 1) / n);
  long long koncowka = l % n;
  if (koncowka == 0) koncowka = n;
  int last = -2, nr = 0;
  for (auto it : input) {
    if (it.first != last) {
      last = it.first;
      nr++;
    }
    count[nr]++;
    if (it.second <= koncowka) {
      countEnd[nr]++;
    }
    tab[it.second] = nr;
  }
  long long wyn = 0;
  long long ileKawalkow = (l - 1) / n;
  for (int i = 1; i <= nr; i++) prev[i] = 1;
  for (int dl = 1; dl <= maxdl; dl++) {
    for (int num = 1; num <= nr; num++) {
      dp[num] = prev[num];
      wyn += (((count[num] * (ileKawalkow - dl + 1) + countEnd[num])) % mod) *
             dp[num];
      wyn %= mod;
      dp[num] *= count[num];
      dp[num] += dp[num - 1];
      dp[num] %= mod;
    }
    std::swap(dp, prev);
  }
  printf("%lld", wyn);
  return 0;
}

```