#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007LL;
const int N = 1000005;
long long arr[N];
long long sorted[N];
long long counts[N];
long long countLeftover[N];
map<long long, long long> condenseMap;
long long dp1[N];
long long cum[N];
long long dp2[N];
long long rec(int i, int z, int k, int maxK, int n, int len, vector<int> &vec) {
  long long ans = 0;
  if (k > 0) ans++;
  if (k < maxK) {
    int brrr = i / n;
    for (int j = (brrr + 1) * n; j < len && j < (brrr + 2) * n; j++) {
      if (vec[j] >= z) {
        ans += rec(j, vec[j], k + 1, maxK, n, len, vec);
      }
    }
  }
  return ans;
}
long long bruteForce(int len, int n, int maxK) {
  vector<int> vec;
  for (int i = 0; i < len; i++) {
    vec.push_back((int)arr[i % n]);
  }
  long long ans = 0;
  for (int i = -n; i < len; i += n) {
    ans += rec(i, -1, 0, maxK, n, len, vec);
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  long long lInput;
  int kInput;
  cin >> n >> lInput >> kInput;
  for (int i = 0; i < n; i++) cin >> arr[i];
  long long numFullBlocks = lInput / n;
  for (int i = 0; i < n; i++) sorted[i] = arr[i];
  sort(&sorted[0], &sorted[n]);
  int curr = 0;
  counts[curr] = 0;
  condenseMap[sorted[0]] = curr;
  counts[curr]++;
  for (int i = 1; i < n; i++) {
    if (sorted[i] != sorted[i - 1]) {
      curr++;
      counts[curr] = 0;
      condenseMap[sorted[i]] = curr;
    }
    counts[curr]++;
  }
  int numUniq = curr + 1;
  int maxk = (int)min((long long)kInput, numFullBlocks);
  for (int i = 0; i < numUniq; i++) countLeftover[i] = 0;
  if ((lInput % n) > 0) {
    int x = (int)(lInput % n);
    for (int i = 0; i < x; i++) {
      countLeftover[condenseMap[arr[i]]]++;
    }
  }
  long long ans = 0;
  for (int i = 0; i < numUniq; i++) {
    dp1[i] = 0;
    cum[i] = 1;
  }
  for (int k = 1; k <= maxk; k++) {
    for (int i = 0; i < numUniq; i++) {
      dp2[i] = (cum[i] * counts[i]) % mod;
      ans = (ans + dp2[i] * ((numFullBlocks + 1 - k) % mod)) % mod;
      ans = (ans + cum[i] * countLeftover[i]) % mod;
    }
    for (int i = 0; i < numUniq; i++) dp1[i] = dp2[i];
    cum[0] = dp1[0];
    for (int i = 1; i < numUniq; i++) {
      cum[i] = (cum[i - 1] + dp1[i]) % mod;
    }
  }
  if (lInput / n < kInput && (lInput % n) > 0) {
    int x = (int)(lInput % n);
    for (int i = 0; i < x; i++) {
      ans = (ans + cum[condenseMap[arr[i]]]) % mod;
    }
  }
  cout << ans << endl;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 = 1000000007LL;
const int N = 1000005;
long long arr[N];
long long sorted[N];
long long counts[N];
long long countLeftover[N];
map<long long, long long> condenseMap;
long long dp1[N];
long long cum[N];
long long dp2[N];
long long rec(int i, int z, int k, int maxK, int n, int len, vector<int> &vec) {
  long long ans = 0;
  if (k > 0) ans++;
  if (k < maxK) {
    int brrr = i / n;
    for (int j = (brrr + 1) * n; j < len && j < (brrr + 2) * n; j++) {
      if (vec[j] >= z) {
        ans += rec(j, vec[j], k + 1, maxK, n, len, vec);
      }
    }
  }
  return ans;
}
long long bruteForce(int len, int n, int maxK) {
  vector<int> vec;
  for (int i = 0; i < len; i++) {
    vec.push_back((int)arr[i % n]);
  }
  long long ans = 0;
  for (int i = -n; i < len; i += n) {
    ans += rec(i, -1, 0, maxK, n, len, vec);
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  long long lInput;
  int kInput;
  cin >> n >> lInput >> kInput;
  for (int i = 0; i < n; i++) cin >> arr[i];
  long long numFullBlocks = lInput / n;
  for (int i = 0; i < n; i++) sorted[i] = arr[i];
  sort(&sorted[0], &sorted[n]);
  int curr = 0;
  counts[curr] = 0;
  condenseMap[sorted[0]] = curr;
  counts[curr]++;
  for (int i = 1; i < n; i++) {
    if (sorted[i] != sorted[i - 1]) {
      curr++;
      counts[curr] = 0;
      condenseMap[sorted[i]] = curr;
    }
    counts[curr]++;
  }
  int numUniq = curr + 1;
  int maxk = (int)min((long long)kInput, numFullBlocks);
  for (int i = 0; i < numUniq; i++) countLeftover[i] = 0;
  if ((lInput % n) > 0) {
    int x = (int)(lInput % n);
    for (int i = 0; i < x; i++) {
      countLeftover[condenseMap[arr[i]]]++;
    }
  }
  long long ans = 0;
  for (int i = 0; i < numUniq; i++) {
    dp1[i] = 0;
    cum[i] = 1;
  }
  for (int k = 1; k <= maxk; k++) {
    for (int i = 0; i < numUniq; i++) {
      dp2[i] = (cum[i] * counts[i]) % mod;
      ans = (ans + dp2[i] * ((numFullBlocks + 1 - k) % mod)) % mod;
      ans = (ans + cum[i] * countLeftover[i]) % mod;
    }
    for (int i = 0; i < numUniq; i++) dp1[i] = dp2[i];
    cum[0] = dp1[0];
    for (int i = 1; i < numUniq; i++) {
      cum[i] = (cum[i - 1] + dp1[i]) % mod;
    }
  }
  if (lInput / n < kInput && (lInput % n) > 0) {
    int x = (int)(lInput % n);
    for (int i = 0; i < x; i++) {
      ans = (ans + cum[condenseMap[arr[i]]]) % mod;
    }
  }
  cout << ans << endl;
}

```