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 MAXN = 1111111;
const long long MOD = 1000000007LL;
int N, K;
long long L, Pos;
long long Num[MAXN];
int NumRank[MAXN];
long long DP[MAXN], SUM, ANS = 0LL;
long long sum(long long a, long long b) {
  long long ret = a + b;
  if (ret >= MOD) ret -= MOD;
  return ret;
}
void RankNum(int l, int r) {
  int i = l, j = r;
  long long test = Num[NumRank[(l + r) >> 1]];
  while (i <= j) {
    while (Num[NumRank[i]] < test) ++i;
    while (Num[NumRank[j]] > test) --j;
    if (i <= j) {
      swap(NumRank[i], NumRank[j]);
      ++i;
      --j;
    }
  }
  if (i < r) RankNum(i, r);
  if (l < j) RankNum(l, j);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> N >> L >> K;
  for (int i = 1; i <= N; ++i) cin >> Num[i];
  for (int i = 1; i <= N; ++i) NumRank[i] = i;
  RankNum(1, N);
  for (int k = 1; k <= K; ++k) {
    SUM = 0LL;
    if (k == 1) SUM = 1LL;
    for (int i = 1, j, sp = 1; i <= N; ++i) {
      j = NumRank[i];
      Pos = (long long)((k - 1) * N + j);
      while (sp <= N && Num[NumRank[sp]] <= Num[j]) SUM = sum(SUM, DP[sp++]);
      if (Pos > L)
        DP[i] = 0LL;
      else
        DP[i] = SUM;
      ANS = sum(ANS, (((L - Pos) / N + 1) % MOD * DP[i]) % MOD);
    }
  }
  cout << ANS << endl;
  return 0;
}
