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>.
/**
 * @author derrick20
 */
import java.io.*;
import java.util.*;

public class DuffInBeachPairs{
    public static void main(String[] args) throws Exception {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);

//        generate();
        int N = sc.nextInt();
        long l = sc.nextLong();
        int K = sc.nextInt();
//        long start = System.currentTimeMillis();
        long blocks = l / N;
        long residue = l % N;

//        if (K == 1) {
//            out.println(l % mod);
//            out.close();
//            return;
//        }

        Integer[] original = new Integer[N];
        Integer[] sorted = new Integer[N];
        for (int i = 0; i < N; i++) {
            int v = sc.nextInt();
            original[i] = v;
            sorted[i] = v;
        }
        Arrays.sort(sorted);
        HashMap<Integer, Integer> compress = new HashMap<>();
        for (int i = 0; i < N; i++) {
            compress.put(sorted[i], i + 1);
        }
        for (int i = 0; i < N; i++) {
            sorted[i] = compress.get(sorted[i]); // map it onto it's sorted index
            original[i] = compress.get(original[i]);
        }
        // now it's basically a permutation, which works!
        int max = N;
        long[][] dp = new long[K + 1][max + 1];
        for (int v = 1, ptr = 0; v <= max; v++) {
            dp[1][v] = dp[1][v - 1];
            while (ptr < N && sorted[ptr] == v) {
                dp[1][v]++;
                ptr++;
            }
        }

        long blockAns = ((blocks - 1 + 1) * dp[1][max]) % mod;
        for (int i = 2; i <= K; i++) {
            for (int v = 1, ptr = 0; v <= max; v++) {
                dp[i][v] = dp[i][v - 1];
                while (ptr < N && sorted[ptr] == v) {
                    dp[i][v] += dp[i - 1][v];
                    if (dp[i][v] >= mod) {
                        dp[i][v] -= mod;
                    }
                    ptr++;
                }
            }
            // anything less or equal can transition here
            // we can slide it around any of the FULL-sized blocks
            // only if it's actually possible though!
            //Todo AHHH
            if (blocks - i + 1 > 0) {
                long addedWays = (((blocks - i + 1) % mod) * dp[i][max]) % mod;
                blockAns = (blockAns + addedWays) % mod;
            }
//                System.out.println("Added for size i: " + addedWays);
        }

        long residueAns = 0;
        // now, we deal with the small cases on the little edge:
        for (int res = 0; res < residue; res++) {
            int val = original[res];

            // no ways to slide this!
            // the last one is fixed, so we iterate to K - 1, the rest is glued to it!
            residueAns++; // we can use a single val
            // we can't go further than using each block
            for (int i = 1; i <= Math.min(K - 1, blocks); i++) {
                residueAns = (residueAns + dp[i][val]);
                if (residueAns >= mod) {
                    residueAns -= mod;
                }
            }
        }
        long ans = (blockAns + residueAns) % mod;
        out.println(ans);
//        out.println((System.currentTimeMillis() - start) / 1000.0);
        out.close();
    }

    static void generate() {
        int N = (int) 1e5;//(int) (Math.random() * 10);
        int l = 1;//(int) (Math.random() * 20);
        int k = 1;//(int) (Math.random() * 10);
        int[] a = new int[N];
        for (int i = 0; i < N; i++) {
            a[i] = (int) (Math.random() * 10000000 + 1);
        }
        System.out.println(N + " " + l + " " + k);
        for (int i = 0; i < N; i++) {
            System.out.print(a[i] + " ");
        }
        System.out.println();
    }

    static long mod = (long) 1e9 + 7;
    static class Pair {
        int idx, val;
        public Pair(int ii, int vv) {
            idx = ii; val = vv;
        }
    }

    static class FastScanner {
        private int BS = 1<<16;
        private char NC = (char)0;
        private byte[] buf = new byte[BS];
        private int bId = 0, size = 0;
        private char c = NC;
        private double cnt = 1;
        private BufferedInputStream in;

        public FastScanner() {
            in = new BufferedInputStream(System.in, BS);
        }

        public FastScanner(String s) {
            try {
                in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
            }
            catch (Exception e) {
                in = new BufferedInputStream(System.in, BS);
            }
        }

        private char getChar(){
            while(bId==size) {
                try {
                    size = in.read(buf);
                }catch(Exception e) {
                    return NC;
                }
                if(size==-1)return NC;
                bId=0;
            }
            return (char)buf[bId++];
        }

        public int nextInt() {
            return (int)nextLong();
        }

        public int[] nextInts(int N) {
            int[] res = new int[N];
            for (int i = 0; i < N; i++) {
                res[i] = (int) nextLong();
            }
            return res;
        }

        public long[] nextLongs(int N) {
            long[] res = new long[N];
            for (int i = 0; i < N; i++) {
                res[i] = nextLong();
            }
            return res;
        }

        public long nextLong() {
            cnt=1;
            boolean neg = false;
            if(c==NC)c=getChar();
            for(;(c<'0' || c>'9'); c = getChar()) {
                if(c=='-')neg=true;
            }
            long res = 0;
            for(; c>='0' && c <='9'; c=getChar()) {
                res = (res<<3)+(res<<1)+c-'0';
                cnt*=10;
            }
            return neg?-res:res;
        }

        public double nextDouble() {
            double cur = nextLong();
            return c!='.' ? cur:cur+nextLong()/cnt;
        }

        public double[] nextDoubles(int N) {
            double[] res = new double[N];
            for (int i = 0; i < N; i++) {
                res[i] = nextDouble();
            }
            return res;
        }

        public String next() {
            StringBuilder res = new StringBuilder();
            while(c<=32)c=getChar();
            while(c>32) {
                res.append(c);
                c=getChar();
            }
            return res.toString();
        }

        public String nextLine() {
            StringBuilder res = new StringBuilder();
            while(c<=32)c=getChar();
            while(c!='\n') {
                res.append(c);
                c=getChar();
            }
            return res.toString();
        }

        public boolean hasNext() {
            if(c>32)return true;
            while(true) {
                c=getChar();
                if(c==NC)return false;
                else if(c>32)return true;
            }
        }
    }

    static void ASSERT(boolean assertion, String message) {
        if (!assertion) throw new AssertionError(message);
    }
}