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>
#pragma comment(linker, "/STACK:1024000000,1024000000")
using namespace std;
const long long LINF = (1LL << 61);
const int INF = 1 << 28;
const int NS = 2111111;
const int MOD = 1000000007;
struct node {
  int id, v;
};
long long m, n, k;
int a[NS];
long long dp[NS];
long long sum[NS];
node p[NS];
bool cmp(node _a, node _b) { return _a.v < _b.v; }
int main() {
  while (cin >> n >> m >> k) {
    int maxleni = n * k + 5;
    for (int i = 0; i < maxleni; i++) {
      dp[i] = 0;
    }
    for (int i = 0; i < n; i++) {
      scanf("%d", &a[i]);
      p[i].id = i;
      p[i].v = a[i];
      dp[i] = 1;
    }
    sort(p, p + n, cmp);
    long long rest = m % n;
    long long num = (m - rest) / n;
    sum[1] = n;
    for (int i = 2; i <= k; i++) {
      sum[i] = 0;
      long long tot = 0;
      int st = (i - 1) * n;
      int y = 0;
      int pos;
      for (int j = 0; j < n; j++) {
        while (y < n && p[j].v == p[y].v) {
          pos = st + p[y].id;
          tot += dp[pos - n];
          tot %= MOD;
          y++;
        }
        pos = st + p[j].id;
        dp[pos] = tot;
        sum[i] += dp[pos];
        sum[i] %= MOD;
      }
    }
    long long ans = 0;
    int lim = k;
    if (num < lim) lim = num;
    for (int i = 1; i <= lim; i++) {
      long long t = sum[i] * ((num - i + 1) % MOD);
      t %= MOD;
      ans += t;
      ans %= MOD;
    }
    lim = min(k, num + 1);
    for (int i = 0; i < rest; i++) {
      for (int j = 1; j <= lim; j++) {
        int pos = (j - 1) * n + i;
        ans += dp[pos];
        ans %= MOD;
      }
    }
    ans += MOD;
    ans %= MOD;
    cout << ans << endl;
  }
  return 0;
}
