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>.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.FileReader;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author OmarYasser
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, Scanner sc, PrintWriter out) {
            int n = sc.nextInt();
            long l = sc.nextLong();
            int k = sc.nextInt();
            k = (l + n - 1) / n < k ? (int) ((l + n - 1) / n) : k;
            int MOD = (int) 1e9 + 7;
            Integer[] tmp = new Integer[n];
            for (int i = 0; i < n; i++)
                tmp[i] = sc.nextInt();
            int rem = (int) (l % n);
            ArrayList<Integer> remArray = new ArrayList<>();
            for (int i = 0; i < rem; i++)
                remArray.add(tmp[i]);
            Collections.sort(remArray);
            Arrays.sort(tmp);
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = tmp[i];

            long[][] dp = new long[k + 1][n];
            for (int i = 0; i < n; i++) dp[1][i] = 1;

            for (int curK = 2; curK <= k; curK++) {
                int sum = 0, last = 0;
                for (int i = 0; i < n; i++) {
                    while (last < n && a[last] <= a[i]) {
                        sum += dp[curK - 1][last];
                        last++;
                        if (sum >= MOD) sum -= MOD;
                    }
                    dp[curK][i] = sum;
                }
            }


            long[][] dp2 = new long[k + 1][rem];
            for (int i = 0; i < rem; i++) dp2[1][i] = 1;

            for (int curK = 2; curK <= k; curK++) {
                int sum = 0, last = 0;
                for (int i = 0; i < rem; i++) {
                    int cur = remArray.get(i);
                    while (last < n && a[last] <= cur) {
                        sum += dp[curK - 1][last];
                        last++;
                        if (sum >= MOD) sum -= MOD;
                    }
                    dp2[curK][i] = sum;
                }
            }

            long res = l % MOD;
            for (int curK = 2; curK <= k; curK++) {
                long can = l / n - (curK - 1);
                can = ((can % MOD) + MOD) % MOD;
                long here = 0;
                for (int i = 0; i < n; i++) {
                    here += dp[curK][i];
                    if (here >= MOD) here -= MOD;
                }
                here = here * can % MOD;
                res += here;
                if (res >= MOD) res -= MOD;
                for (int i = 0; i < rem; i++) {
                    res += dp2[curK][i];
                    if (res >= MOD) res -= MOD;
                }
            }
            out.println(res);
        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader f) {
            br = new BufferedReader(f);
        }

        public String next() {
            while (st == null || !st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

    }
}

