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>.
//package codeforces.cfr326div2;

import java.io.*;
import java.util.Arrays;
import java.util.Comparator;

/**
 * Created by raggzy on 02-Nov-15.
 */
public class E {
    private static final int MOD = 1000 * 1000 * 1000 + 7;

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        String[] tmp = in.readLine().split(" ");
        int n = Integer.valueOf(tmp[0]);
        long l = Long.valueOf(tmp[1]);
        int k = Integer.valueOf(tmp[2]);
        int[] a = new int[n];
        Integer[] s = new Integer[n];
        tmp = in.readLine().split(" ");
        for (int i = 0; i < n; i++) {
            a[i] = Integer.valueOf(tmp[i]);
            s[i] = i;
        }
        // indexes in values increasing order
        Arrays.sort(s, Comparator.comparingInt((i -> a[i])));
        //
        int[][] f = new int[k + 1][n];
        for (int i = 0; i < n; i++) {
            f[1][i] = 1;
        }
        for (int len = 2; len <= k; len++) {
            int sum = 0;
            int i = 0;
            for (int endIdx = 0; endIdx < n; endIdx++) {
                while (i < n && a[s[i]] <= a[s[endIdx]]) {
                    sum = (sum + f[len - 1][s[i]]) % MOD;
                    i++;
                }
                f[len][s[endIdx]] = sum;
            }
        }
        //
        int result = 0;
        for (int len = 1; len <= k; len++) {
            if (l / n - len + 1 < 0) break;
            for (int end = 0; end < n; end++) {
                long count = l / n - len + 1 + ((end < l % n) ? 1 : 0);
                result = (result + (int) (((count % MOD) * f[len][end]) % MOD)) % MOD;
            }
        }
        System.out.println(result);
    }
}
