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;
using i64 = long long;
using Pii = pair<int, int>;
constexpr int MAX = 2000100;
constexpr int MOD = 1000000007;
inline void Add(i64& a, i64 b, i64 p = MOD) {
  if ((a += b) >= p) a -= p;
}
inline i64 Sub(i64 a, i64 b, i64 p = MOD) {
  if ((a -= b) < 0) a += p;
  return a;
}
struct BIT {
  i64 c[MAX];
  int sz;
  void Init(int n) {
    fill(c, c + n + 1, 0);
    sz = n;
  }
  void Update(int k, i64 v) {
    for (; k <= sz; k += ((k) & -(k))) {
      Add(c[k], v);
    }
  }
  i64 Query(int k) const {
    i64 ret = 0;
    for (; k; k -= ((k) & -(k))) {
      Add(ret, c[k]);
    }
    return ret;
  }
} bit[2];
int a[MAX], b[MAX], x[MAX];
int Solve(int n, int k, i64 l) {
  copy_n(a, n, b);
  sort(b, b + n);
  int m = unique(b, b + n) - b;
  for (int i = 0; i < n; ++i) {
    x[i] = lower_bound(b, b + m, a[i]) - b + 1;
  }
  bit[0].Init(m);
  bit[1].Init(m);
  i64 ret = 0, d = l / n, u = (l + n - 1) / n, r = l % n;
  for (int i = 0; i < n; ++i) {
    bit[0].Update(x[i], 1);
    if (i < r)
      Add(ret, (i64)(d + 1) % MOD);
    else
      Add(ret, (i64)d % MOD);
  }
  for (int i = 1; i < k && i < u; ++i) {
    int t = (i & 1);
    bit[t].Init(n);
    for (int j = 0; j < n; ++j) {
      i64 cur = bit[t ^ 1].Query(x[j]);
      bit[t].Update(x[j], cur);
      if (j < r)
        Add(ret, cur * Sub((d + 1) % MOD, i) % MOD);
      else
        Add(ret, cur * Sub(d % MOD, i) % MOD);
    }
  }
  return (int)ret;
}
int main() {
  int n, k;
  i64 l;
  while (cin >> n >> l >> k) {
    for (int i = 0; i < n; ++i) {
      scanf("%d", &a[i]);
    }
    printf("%d\n", Solve(n, k, l));
  }
  return 0;
}
