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 base = (int)1e9 + 7;
int n, k;
long long l;
int a[1000005];
int gt[1000005];
long long res = 0;
long long mul(long long a, int b) {
  long long re = 0;
  long long c = a;
  while (b) {
    if (b & 1) re = (re + c) % base;
    c = (c + c) % base;
    b /= 2;
  }
  return re;
}
int main() {
  cin >> n >> l >> k;
  vector<vector<int> > f(k + 5, vector<int>(n + 5));
  vector<vector<int> > sum(k + 5, vector<int>(n + 5));
  vector<int> g(n + 5);
  vector<int> b(n + 5);
  map<int, int> Map;
  Map.clear();
  for (int i = 1; i <= n; ++i) {
    scanf("%d", a + i);
    b[i] = a[i];
  }
  sort(a + 1, a + 1 + n);
  for (int i = n; i >= 1; --i) {
    if (a[i] == a[i + 1])
      g[i] = g[i + 1];
    else
      g[i] = i;
    Map[a[i]] = g[i];
    sum[0][i] = 1;
  }
  for (int i = 1; i <= k; ++i) {
    for (int j = 1; j <= n; ++j) {
      f[i][j] = sum[i - 1][g[j]];
      sum[i][j] = (sum[i][j - 1] + f[i][j]) % base;
    }
    long long tmp1 = 0;
    for (int j = 1; j <= l % n; ++j)
      tmp1 = (tmp1 + sum[i - 1][Map[b[j]]]) % base;
    long long t1 = l / n + (l % n != 0);
    long long tmp = 0;
    if (t1 >= i) {
      if (l % n == 0)
        tmp = mul(t1 - i + 1, sum[i][n]);
      else
        tmp = (mul(t1 - i, sum[i][n]) + tmp1) % base;
    }
    res = (res + tmp) % base;
  }
  cout << res << endl;
}
