#include <bits/stdc++.h>
using namespace std;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cerr << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
const long long int mod = 1000000007;
const int N = 1000005;
vector<vector<long long int> > dp, sum, vis, dp1;
int a[N], b[N];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n, l, k;
  cin >> n >> l >> k;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    b[i] = a[i];
  }
  sort(a, a + n);
  dp.resize(k + 1);
  sum.resize(k + 1);
  vis.resize(k + 1);
  dp1.resize(k + 1);
  for (int i = 0; i <= k; i++) {
    dp[i].resize(n + 1);
    sum[i].resize(n + 1);
    vis[i].resize(n + 1);
    dp1[i].resize(n + 1);
    for (int j = 0; j <= n; j++) {
      dp[i][j] = sum[i][j] = vis[i][j] = 0;
    }
  }
  dp[1][0] = 1;
  sum[1][0] = 1;
  for (int i = 1; i < n; i++) {
    dp[1][i] = 1;
    sum[1][i] = sum[1][i - 1] + 1;
  }
  long long int blocks = l / n;
  long long int ii = l % n;
  long long int ans = 0;
  ans += l;
  ans %= mod;
  for (int i = 2; i <= k; i++) {
    for (int j = 0; j < n; j++) {
      int pt = upper_bound(a, a + n, b[j]) - a;
      pt--;
      dp1[i][j] = sum[i - 1][pt];
      long long int tp = blocks + 1 - i;
      if (j < ii) {
        tp++;
        if (tp > 0) {
          tp %= mod;
          long long int tmp = (tp * dp1[i][j]) % mod;
          ans += tmp;
          ans %= mod;
        }
      } else {
        if (tp > 0) {
          tp %= mod;
          long long int tmp = (tp * dp1[i][j]) % mod;
          ans += tmp;
          ans %= mod;
        }
      }
    }
    for (int j = 0; j < n; j++) {
      int pt1 = upper_bound(a, a + n, b[j]) - a;
      int pt2 = lower_bound(a, a + n, b[j]) - a;
      if (!vis[i][pt2])
        for (int z = pt2; z < pt1; z++) {
          dp[i][z] = dp1[i][j];
          vis[i][z] = 1;
        }
    }
    sum[i][0] = dp[i][0];
    for (int j = 1; j < n; j++) {
      sum[i][j] = (sum[i][j - 1] + dp[i][j]) % mod;
    }
  }
  cout << ans << "\n";
  return 0;
}

### 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;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cerr << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
const long long int mod = 1000000007;
const int N = 1000005;
vector<vector<long long int> > dp, sum, vis, dp1;
int a[N], b[N];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n, l, k;
  cin >> n >> l >> k;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    b[i] = a[i];
  }
  sort(a, a + n);
  dp.resize(k + 1);
  sum.resize(k + 1);
  vis.resize(k + 1);
  dp1.resize(k + 1);
  for (int i = 0; i <= k; i++) {
    dp[i].resize(n + 1);
    sum[i].resize(n + 1);
    vis[i].resize(n + 1);
    dp1[i].resize(n + 1);
    for (int j = 0; j <= n; j++) {
      dp[i][j] = sum[i][j] = vis[i][j] = 0;
    }
  }
  dp[1][0] = 1;
  sum[1][0] = 1;
  for (int i = 1; i < n; i++) {
    dp[1][i] = 1;
    sum[1][i] = sum[1][i - 1] + 1;
  }
  long long int blocks = l / n;
  long long int ii = l % n;
  long long int ans = 0;
  ans += l;
  ans %= mod;
  for (int i = 2; i <= k; i++) {
    for (int j = 0; j < n; j++) {
      int pt = upper_bound(a, a + n, b[j]) - a;
      pt--;
      dp1[i][j] = sum[i - 1][pt];
      long long int tp = blocks + 1 - i;
      if (j < ii) {
        tp++;
        if (tp > 0) {
          tp %= mod;
          long long int tmp = (tp * dp1[i][j]) % mod;
          ans += tmp;
          ans %= mod;
        }
      } else {
        if (tp > 0) {
          tp %= mod;
          long long int tmp = (tp * dp1[i][j]) % mod;
          ans += tmp;
          ans %= mod;
        }
      }
    }
    for (int j = 0; j < n; j++) {
      int pt1 = upper_bound(a, a + n, b[j]) - a;
      int pt2 = lower_bound(a, a + n, b[j]) - a;
      if (!vis[i][pt2])
        for (int z = pt2; z < pt1; z++) {
          dp[i][z] = dp1[i][j];
          vis[i][z] = 1;
        }
    }
    sum[i][0] = dp[i][0];
    for (int j = 1; j < n; j++) {
      sum[i][j] = (sum[i][j - 1] + dp[i][j]) % mod;
    }
  }
  cout << ans << "\n";
  return 0;
}

```