#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
long long powmod(long long a, long long b) {
  long long res = 1;
  a %= mod;
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % mod;
    a = a * a % mod;
  }
  return res;
}
long long n, l, k, a, idx, idx1, pSum;
map<long long, int> input, input1;
long long dp[1000005][2];
int main() {
  memset(dp, 0, sizeof(dp));
  cin >> n >> l >> k;
  long long lastBlk = (n < l) ? (l % n) : l;
  long long repCnt = (l - lastBlk) / n;
  for (int i = 0; i < (int)n; i++) {
    cin >> a;
    input[a]++;
    if (i < lastBlk) input1[a]++;
  }
  idx = 0;
  for (map<long long, int>::iterator it = input.begin(); it != input.end();
       it++, idx++) {
    dp[idx][0] = it->second;
  }
  long long ans = l % mod;
  bool pos = 1;
  int ePos = min(repCnt, k - 1);
  for (int i = 1; i < (int)ePos + 1; i++) {
    idx = pSum = idx1 = 0;
    map<long long, int>::iterator it1 = input.begin();
    for (map<long long, int>::iterator it = input1.begin(); it != input1.end();
         it++, idx++) {
      while (it1 != input.end()) {
        if (it1->first > it->first) break;
        pSum += dp[idx1++][!pos];
        pSum %= mod;
        it1++;
      }
      ans += it->second * pSum;
      ans %= mod;
    }
    pSum = idx = 0;
    for (map<long long, int>::iterator it = input.begin(); it != input.end();
         it++, idx++) {
      pSum += dp[idx][!pos];
      pSum %= mod;
      dp[idx][pos] = pSum * it->second;
      dp[idx][pos] %= mod;
      ans += dp[idx][pos] * ((repCnt - i) % mod);
      ans %= mod;
    }
    pos = !pos;
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Your task is to create a Cpp solution to the following problem:

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>.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
long long powmod(long long a, long long b) {
  long long res = 1;
  a %= mod;
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % mod;
    a = a * a % mod;
  }
  return res;
}
long long n, l, k, a, idx, idx1, pSum;
map<long long, int> input, input1;
long long dp[1000005][2];
int main() {
  memset(dp, 0, sizeof(dp));
  cin >> n >> l >> k;
  long long lastBlk = (n < l) ? (l % n) : l;
  long long repCnt = (l - lastBlk) / n;
  for (int i = 0; i < (int)n; i++) {
    cin >> a;
    input[a]++;
    if (i < lastBlk) input1[a]++;
  }
  idx = 0;
  for (map<long long, int>::iterator it = input.begin(); it != input.end();
       it++, idx++) {
    dp[idx][0] = it->second;
  }
  long long ans = l % mod;
  bool pos = 1;
  int ePos = min(repCnt, k - 1);
  for (int i = 1; i < (int)ePos + 1; i++) {
    idx = pSum = idx1 = 0;
    map<long long, int>::iterator it1 = input.begin();
    for (map<long long, int>::iterator it = input1.begin(); it != input1.end();
         it++, idx++) {
      while (it1 != input.end()) {
        if (it1->first > it->first) break;
        pSum += dp[idx1++][!pos];
        pSum %= mod;
        it1++;
      }
      ans += it->second * pSum;
      ans %= mod;
    }
    pSum = idx = 0;
    for (map<long long, int>::iterator it = input.begin(); it != input.end();
         it++, idx++) {
      pSum += dp[idx][!pos];
      pSum %= mod;
      dp[idx][pos] = pSum * it->second;
      dp[idx][pos] %= mod;
      ans += dp[idx][pos] * ((repCnt - i) % mod);
      ans %= mod;
    }
    pos = !pos;
  }
  cout << ans << endl;
  return 0;
}

```