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>.
#include <bits/stdc++.h>
using namespace std;
const int N = 1314520;
const long long MOD = 1e9 + 7;
int oldArr[N], newArr[N];
template <class T>
inline void AddWithMod(T &a, const T &b) {
  a += b;
  a %= MOD;
}
int main() {
  long long n, l, k;
  while (cin >> n >> l >> k) {
    vector<vector<long long> > dp(k + 1, vector<long long>(n, 0));
    for (int i = 0; i < n; ++i) {
      scanf("%d", oldArr + i);
      newArr[i] = oldArr[i];
    }
    if (l <= n) {
      cout << l << endl;
      continue;
    }
    long long r = l % n;
    sort(newArr, newArr + n);
    sort(oldArr, oldArr + r);
    long long c = l / n;
    long long answer = l % MOD;
    cerr << "c " << c << endl;
    for (int i = 0; i < n; ++i) {
      dp[1][i] = 1;
    }
    for (int i = 2; i <= k; ++i) {
      long long sum, sum2;
      sum = sum2 = 0;
      for (int j = 0, t = 0; j < n; ++j) {
        while (t < n && newArr[t] <= newArr[j]) {
          AddWithMod(sum, dp[i - 1][t]);
          ++t;
        }
        dp[i][j] = sum;
        AddWithMod(sum2, sum);
      }
      answer = (answer + sum2 * max(0LL, (c - i + 1) % MOD)) % MOD;
      if (c - i + 1 >= 0) {
        sum = 0;
        for (int j = 0, t = 0; j < r; ++j) {
          while (t < n && newArr[t] <= oldArr[j]) {
            AddWithMod(sum, dp[i - 1][t]);
            ++t;
          }
          AddWithMod(answer, sum);
        }
      }
    }
    cout << answer << endl;
  }
  return 0;
}
