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.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.Map;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

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

    static class DDuffInBeach {
        int mod = 1000000007;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();

            long l = in.nextLong();

            int k = in.nextInt();

            long rem = n;
            long ak = k;
            if (l < n * k) {
                if (l % n == 0) {
                    ak = l / n;
                } else {
                    rem = l % n;
                    ak = l / n;
                }
            } else {
                if (l % n != 0) {
                    rem = l % n;
                }
            }

            Integer[] a = new Integer[n];
            Integer[] b = new Integer[n];

            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
                b[i] = a[i];
            }

            Arrays.sort(b);

            Map<Integer, Integer> map = new HashMap<>();

            int z = 0;
            for (int i = 0; i < n; i++) {
                if (!map.containsKey(b[i]))
                    map.put(b[i], z++);
            }

            int an = z;

            int[] m1 = new int[an];
            int[] m2 = new int[an];

            for (int i = 0; i < n; i++) {
                m1[map.get(a[i])]++;
            }
            for (int i = 0; i < rem; i++) {
                m2[map.get(a[i])]++;
            }


            long[][] dp = new long[(int) ak][an];
            long[][] dpp = new long[(int) ak][an];

            if (ak > 0) {
                for (int i = 0; i < an; i++) {
                    dp[0][i] = m1[i];
                }


                dpp[0] = in.calculatePrefixSum(dp[0]);
            }

            for (int i = 1; i < ak; i++) {
                for (int j = 0; j < an; j++) {
                    long val = m1[j];
                    dp[i][j] = (val) * dpp[i - 1][j];
                    dp[i][j] %= mod;
                }
                dpp[i] = in.calculatePrefixSum(dp[i], mod);
            }

            long ans = 0;//dpp[(int) ak - 1][(int) an - 1];

            long times = l / n;
            times %= mod;
            for (int i = 0; i < an; i++) {
                for (int j = 1; j <= ak; j++) {
                    ans += (dp[j - 1][i] * (times - j + 1)) % mod;
                    ans %= mod;
                }
            }
//        if (ak > 1) {
//            ans += dp[(int) ak - 2][n - 1] - dp[(int) ak - 2][(int) rem - 1];
//            ans %= mod;
//
//            if (ans < 0) {
//                ans += mod;
//            }
//        }

            if (rem != n) {
                if (ak < k) {
                    ak++;
                }
                long[][] dp2 = new long[(int) ak][n];
                for (int j = 0; j < an; j++) {
                    long val = m2[j];
                    //ans += ((val) * dpp[(int) ak - 1][j] + dp[(int) ak - 1][j] + val) % mod;
                    dp2[0][j] = val;
                    ans += dp2[0][j];
                    ans %= mod;
                }
                for (int i = 1; i < ak; i++) {
                    for (int j = 0; j < an; j++) {
                        long val = m2[j];
                        dp2[i][j] = (val) * dpp[i - 1][j];
                        dp2[i][j] %= mod;
                        ans += dp2[i][j];
                        ans %= mod;
                    }
                }
            }

            if (ans < 0) {
                ans += mod;
            }
            out.println(ans);
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public long[] calculatePrefixSum(long[] a) {
            int n = a.length;

            long[] prefixSum = new long[n];

            prefixSum[0] = a[0];

            for (int i = 1; i < n; i++) {
                prefixSum[i] = prefixSum[i - 1] + a[i];
            }

            return prefixSum;
        }

        public long[] calculatePrefixSum(long[] a, long mod) {
            int n = a.length;

            long[] prefixSum = new long[n];

            prefixSum[0] = a[0] % mod;

            for (int i = 1; i < n; i++) {
                prefixSum[i] = prefixSum[i - 1] + a[i];
                prefixSum[i] %= mod;
            }

            return prefixSum;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

