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.*;
import java.util.*;

public class D {

    MyScanner in;
    PrintWriter out;

    public static void main(String[] args) throws Exception {
        new D().run();
    }

    public void run() throws Exception {
        in = new MyScanner();
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    final static long MODULO = 1000000007;

    static class P implements Comparable<P>{
        int i, a;
        public P(int a, int i) {
            this.a = a;
            this.i = i;
        }

        @Override
        public int compareTo(P o) {
            return this.a - o.a;
        }
    }

    static class Q {
        int x;
        public Q(int x) {
            this.x = x;
        }
    }

    public void solve() throws Exception {
        int n = in.nextInt();
        long l = in.nextLong();
        int k = in.nextInt();
        long s = l / n;
        P[] a = new P[n];
        for (int i = 0; i < n; i++) {
            a[i] = new P(in.nextInt(), i);
        }
        Arrays.sort(a);

        long[][] d = new long[k + 1][n];
        for (int i = 0; i < n; i++) {
            d[1][i] = 1;
        }
        for (int x = 2; x <= k; x++) {
            int i = 0;
            long sum = 0;
            while (i < n) {
                int j = i;
                while (j < n && a[i].a == a[j].a) {
                    sum = (sum + d[x - 1][a[j].i]) % MODULO;
                    j++;
                }
                for (int f = i; f < j; f++) {
                    d[x][a[f].i] = sum;
                }
                i = j;
            }
        }

        long ans = 0;
        int m = (int) (l % n);
        for (int x = 1; x <= k; x++) {
            if (x <= s + 1) {
                for (int i = 0; i < m; i++) {
                    ans = (ans + ((s - x + 2) % MODULO) * d[x][i]) % MODULO;
                }
            }
            if (x <= s) {
                for (int i = m; i < n; i++) {
                    ans = (ans + ((s - x + 1) % MODULO) * d[x][i]) % MODULO;
                }
            }
        }
        out.println(ans);
    }

    class MyScanner {

        BufferedReader br;
        StringTokenizer st;

        public MyScanner() throws Exception {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() throws Exception {
            while ((st == null) || (!st.hasMoreTokens())) {
                String t = br.readLine();
                if (t == null) {
                    return null;
                }
                st = new StringTokenizer(t);
            }
            return st.nextToken();
        }

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

        double nextDouble() throws Exception {
            return Double.parseDouble(next());
        }

        boolean nextBoolean() throws Exception {
            return Boolean.parseBoolean(next());
        }

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