#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T &x) {
  char c;
  bool nega = 0;
  while ((!isdigit(c = getchar())) && (c != '-'))
    ;
  if (c == '-') {
    nega = 1;
    c = getchar();
  }
  x = c - 48;
  while (isdigit(c = getchar())) x = x * 10 + c - 48;
  if (nega) x = -x;
}
template <typename T>
inline void writep(T x) {
  if (x > 9) writep(x / 10);
  putchar(x % 10 + 48);
}
template <typename T>
inline void write(T x) {
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  writep(x);
}
template <typename T>
inline void writeln(T x) {
  write(x);
  putchar('\n');
}
long long l;
int n, k, m;
int a[1000000];
pair<int, int> f[1000000];
int sum[1000000];
const int base = 1000000007;
int main() {
  read(n);
  read(l);
  read(k);
  for (int i = 0; i <= n - 1; i++) read(a[i]);
  m = (n * k);
  for (int i = 0; i <= m - 1; i++) f[i] = make_pair(a[i % n], i);
  sort(f, f + m);
  long long ans = 0;
  for (int i = 0; i <= m - 1; i++) {
    int k = f[i].second / n;
    long long p;
    if (f[i].second < n)
      p = 1;
    else
      p = sum[k - 1];
    sum[k] = (sum[k] + p) % base;
    if (f[i].second < l) {
      long long r = (l - f[i].second - 1) / n + 1;
      r %= base;
      ans = (ans + r * p % base) % base;
    }
  }
  writeln(ans);
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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;
template <typename T>
inline void read(T &x) {
  char c;
  bool nega = 0;
  while ((!isdigit(c = getchar())) && (c != '-'))
    ;
  if (c == '-') {
    nega = 1;
    c = getchar();
  }
  x = c - 48;
  while (isdigit(c = getchar())) x = x * 10 + c - 48;
  if (nega) x = -x;
}
template <typename T>
inline void writep(T x) {
  if (x > 9) writep(x / 10);
  putchar(x % 10 + 48);
}
template <typename T>
inline void write(T x) {
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  writep(x);
}
template <typename T>
inline void writeln(T x) {
  write(x);
  putchar('\n');
}
long long l;
int n, k, m;
int a[1000000];
pair<int, int> f[1000000];
int sum[1000000];
const int base = 1000000007;
int main() {
  read(n);
  read(l);
  read(k);
  for (int i = 0; i <= n - 1; i++) read(a[i]);
  m = (n * k);
  for (int i = 0; i <= m - 1; i++) f[i] = make_pair(a[i % n], i);
  sort(f, f + m);
  long long ans = 0;
  for (int i = 0; i <= m - 1; i++) {
    int k = f[i].second / n;
    long long p;
    if (f[i].second < n)
      p = 1;
    else
      p = sum[k - 1];
    sum[k] = (sum[k] + p) % base;
    if (f[i].second < l) {
      long long r = (l - f[i].second - 1) / n + 1;
      r %= base;
      ans = (ans + r * p % base) % base;
    }
  }
  writeln(ans);
}

```