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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Artem Gilmudinov
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Reader in = new Reader(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, Reader in, PrintWriter out) {
            int n, k;
            long l;
            n = in.ni();
            l = in.nl();
            k = in.ni();
            PairInt[] nums = new PairInt[n];
            for (int i = 0; i < n; i++) {
                nums[i] = new PairInt(in.ni(), i);
            }
            final int mod = 1_000_000_007;
            Arrays.sort(nums, new Comparator<PairInt>() {

                public int compare(PairInt o1, PairInt o2) {
                    return o1.x - o2.x;
                }
            });
            int[][] dp = new int[k][n];
            int[] sum = new int[n + 1];
            for (int i = 0; i < n; i++) {
                if (nums[i].y < l) {
                    dp[0][i] = 1;
                }
            }

            for (int i = 1; i <= n; i++) {
                sum[i] = (sum[i - 1] + dp[0][i - 1]) % mod;
            }
            int[] pref = new int[n + 1];
            for (int i = 0; i < n; ) {
                int j = i;
                for (; j < n; j++) {
                    if (nums[i].x != nums[j].x) {
                        break;
                    }
                }
                for (int z = i; z < j; z++) {
                    pref[z + 1] = pref[i] + (j - i);
                }
                i = j;
            }
            long temp;
            for (int i = 1; i < k; i++) {
                temp = (long) i * n;
                for (int j = 0; j < n; j++) {
                    if (temp + nums[j].y < l) {
                        dp[i][j] = (dp[i][j] + sum[pref[j + 1]]) % mod;
                    }
                }
                for (int j = 1; j <= n; j++) {
                    sum[j] = (sum[j - 1] + dp[i][j - 1]) % mod;
                }
            }
            long ans = 0;
            long cnt, diff;
            for (int i = 0; i < k; i++) {
                for (int j = 0; j < n; j++) {
                    if (dp[i][j] != 0) {
                        diff = (long) i * n + nums[j].y;
                        if ((l - diff) % n == 0) {
                            cnt = (l - diff) / n;
                        } else {
                            cnt = (l - diff) / n + 1;
                        }
                        cnt %= mod;
                        ans = (ans + dp[i][j] * cnt) % mod;
                    }
                }
            }
            out.println(ans);
        }

    }

    static class Reader {
        private BufferedReader in;
        private StringTokenizer st = new StringTokenizer("");
        private String delim = " ";

        public Reader(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
        }

        public String next() {
            if (!st.hasMoreTokens()) {
                st = new StringTokenizer(rl());
            }
            return st.nextToken(delim);
        }

        public String rl() {
            try {
                return in.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

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

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

    }

    static class PairInt {
        public int x;
        public int y;

        public PairInt(int x, int y) {
            this.x = x;
            this.y = y;
        }

        public String toString() {
            return x + " " + y;
        }

        public PairInt clone() {
            return new PairInt(x, y);
        }

    }
}

