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>.
#include <bits/stdc++.h>
using namespace std;
int b[1000005];
long long ways[1000005];
long long dp[2][1000005];
long long bit[1000005];
long long query(int indx) {
  long long sum = 0;
  while (indx) {
    sum += bit[indx];
    sum %= 1000000007;
    indx -= (indx & -indx);
  }
  return sum;
}
void update(int indx, long long x) {
  while (indx < 1000005) {
    bit[indx] += x;
    bit[indx] %= 1000000007;
    indx += (indx & -indx);
  }
}
long long int multiply(long long int val, long long int n, long long int mod) {
  long long int q = ((double)val * (double)n / (double)mod);
  long long int res = val * n - mod * q;
  res = (res % mod + mod) % mod;
  return res;
}
int main() {
  int n, k;
  long long l;
  cin >> n >> l >> k;
  vector<int> a(n);
  map<int, int> h;
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    h[a[i]] = 1;
  }
  int cnt = 1;
  for (map<int, int>::iterator i = h.begin(); i != h.end(); i++) {
    i->second = cnt++;
  }
  for (int i = 0; i < n; i++) {
    a[i] = h[a[i]];
  }
  if (n * k > l) {
    int current = 0, prev = 1;
    int blocks = l / n;
    for (int j = 0; j < blocks; j++) {
      for (int i = 0; i < n; i++) {
        dp[current][i] = 0;
      }
      for (int i = 0; i < n; i++) {
        dp[current][i] = query(a[i]) + 1;
        dp[current][i] %= 1000000007;
      }
      for (int i = 0; i < n; i++) {
        update(a[i], (1000000007 - dp[prev][i]));
      }
      for (int i = 0; i < n; i++) {
        update(a[i], dp[current][i]);
      }
      int offset = j * n;
      for (int i = 0; i < n; i++) {
        ways[offset + i] = dp[current][i];
      }
      swap(current, prev);
    }
    for (int i = n * blocks, j = 0; i < l; i++, j++) {
      ways[i] = query(a[j]) + 1;
      ways[i] %= 1000000007;
    }
    long long totalWays = 0;
    for (int i = 0; i < l; i++) {
      totalWays += ways[i];
      totalWays %= 1000000007;
    }
    cout << totalWays << endl;
  } else {
    int current = 0, prev = 1;
    int blocks = k;
    for (int j = 0; j < blocks; j++) {
      for (int i = 0; i < n; i++) {
        dp[current][i] = 0;
      }
      for (int i = 0; i < n; i++) {
        dp[current][i] = query(a[i]) + 1;
        dp[current][i] %= 1000000007;
      }
      for (int i = 0; i < n; i++) {
        update(a[i], (1000000007 - dp[prev][i]));
      }
      for (int i = 0; i < n; i++) {
        update(a[i], dp[current][i]);
      }
      int offset = j * n;
      for (int i = 0; i < n; i++) {
        ways[offset + i] = dp[current][i];
      }
      swap(current, prev);
    }
    long long totalBlocks = l / n;
    long long totalWays = 0;
    for (int j = 0; j < k; j++) {
      int offset = j * n;
      for (int i = 0; i < n; i++) {
        totalWays += ways[offset + i];
        totalWays %= 1000000007;
      }
    }
    long long lastBlockSum = 0;
    for (int i = 0; i < n; i++) {
      lastBlockSum += dp[prev][i];
      lastBlockSum %= 1000000007;
    }
    totalWays += (lastBlockSum * ((totalBlocks - k) % 1000000007)) % 1000000007;
    totalWays %= 1000000007;
    int rem = l % n;
    for (int i = 0; i < rem; i++) {
      totalWays += dp[prev][i];
      totalWays %= 1000000007;
    }
    cout << totalWays << endl;
  }
}
