For technical reasons, some programming languages (Kotlin, C #) will not be available during round 877. ×

B. Duff in Beach
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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,
  • 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, . So all such sequences are: , , , , , , , , and .