#include <bits/stdc++.h>
using namespace std;
namespace IO {
void setIn(string s) { freopen(s.c_str(), "r", stdin); }
void setOut(string s) { freopen(s.c_str(), "w", stdout); }
void setIO(string s = "") {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin.exceptions(cin.failbit);
  if (s.size()) {
    setIn(s + ".inp");
    setOut(s + ".out");
  } else {
  }
}
}  // namespace IO
using namespace IO;
namespace Function {
template <typename T1, typename T2>
void amax(T1 &a, T2 b) {
  if (typeid(a).name() == typeid(int).name() &&
      typeid(b).name() == typeid(long long).name()) {
    cout << "Error on amax";
    exit(0);
  }
  if (a < b) a = b;
}
template <typename T1, typename T2>
void amin(T1 &a, T2 b) {
  if (a > b) a = b;
}
template <typename T>
void compress(vector<T> &a) {
  sort(a.begin(), a.end());
  a.resize(unique(a.begin(), a.end()) - a.begin());
}
template <typename T>
long long sqr(T x) {
  return 1LL * x * x;
}
template <typename T1, typename T2>
long long gcd(T1 a, T2 b) {
  return (b == 0 ? a : gcd(b, a % b));
}
template <typename T1, typename T2>
long long lcm(T1 a, T2 b) {
  return 1LL * a / gcd(a, b) * b;
}
}  // namespace Function
using namespace Function;
namespace Output {
void print(int x) { cout << x << "\n"; }
void print(unsigned int x) { cout << x << "\n"; }
void print(long unsigned int x) { cout << x << "\n"; }
void print(long long x) { cout << x << "\n"; }
void print(unsigned long long x) { cout << x << "\n"; }
void print(float x) { cout << x << "\n"; }
void print(double x) { cout << x << "\n"; }
void print(long double x) { cout << x << "\n"; }
void print(char x) { cout << x << "\n"; }
void print(const char *x) { cout << x << "\n"; }
void print(string x) { cout << x << "\n"; }
void print(bool x) { cout << x << "\n"; }
template <class T, class... Ts>
void print(T t, Ts... ts) {
  cout << t << " ";
  print(ts...);
}
template <typename T1, typename T2>
void print(pair<T1, T2> a) {
  print(a.first, a.second);
}
template <typename T>
void print(T a) {
  for (auto it : a) {
    print(it);
  }
}
template <class T, class... Ts>
void prine(T t, Ts... ts) {
  print(t, ts...);
  exit(0);
}
}  // namespace Output
using namespace Output;
const int dx[] = {1, -1, 0, 0};
const int dy[] = {0, 0, 1, -1};
const int INF = 1e9;
const long long INFL = 1e18;
const int MOD = 1e9 + 7;
const int N = 1e6 + 10;
long long dp[N];
pair<int, int> a[N];
int main() {
  setIO();
  int n, k;
  long long l;
  cin >> n >> l >> k;
  long long Q = l / n;
  long long r = l % n;
  for (int i = 0; i < n; i++) {
    cin >> a[i].first;
    a[i].second = i;
  }
  dp[0] = 1;
  sort(a, a + n);
  long long res = 0;
  for (int len = 0; len < k; len++) {
    if (len > Q) {
      break;
    }
    long long sum = 0;
    int pos = 0;
    for (int i = 0; i < n; i++) {
      while (pos < n && a[pos].first <= a[i].first) {
        sum += dp[pos++];
        sum %= MOD;
      }
      dp[i] = sum;
      res += (dp[i] * ((Q - len) % MOD)) % MOD;
      res %= MOD;
      if (a[i].second < r) {
        res += dp[i];
        res %= MOD;
      }
    }
  }
  print(res);
  return 0;
}

### Prompt

Please create a solution in Cpp 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;
namespace IO {
void setIn(string s) { freopen(s.c_str(), "r", stdin); }
void setOut(string s) { freopen(s.c_str(), "w", stdout); }
void setIO(string s = "") {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin.exceptions(cin.failbit);
  if (s.size()) {
    setIn(s + ".inp");
    setOut(s + ".out");
  } else {
  }
}
}  // namespace IO
using namespace IO;
namespace Function {
template <typename T1, typename T2>
void amax(T1 &a, T2 b) {
  if (typeid(a).name() == typeid(int).name() &&
      typeid(b).name() == typeid(long long).name()) {
    cout << "Error on amax";
    exit(0);
  }
  if (a < b) a = b;
}
template <typename T1, typename T2>
void amin(T1 &a, T2 b) {
  if (a > b) a = b;
}
template <typename T>
void compress(vector<T> &a) {
  sort(a.begin(), a.end());
  a.resize(unique(a.begin(), a.end()) - a.begin());
}
template <typename T>
long long sqr(T x) {
  return 1LL * x * x;
}
template <typename T1, typename T2>
long long gcd(T1 a, T2 b) {
  return (b == 0 ? a : gcd(b, a % b));
}
template <typename T1, typename T2>
long long lcm(T1 a, T2 b) {
  return 1LL * a / gcd(a, b) * b;
}
}  // namespace Function
using namespace Function;
namespace Output {
void print(int x) { cout << x << "\n"; }
void print(unsigned int x) { cout << x << "\n"; }
void print(long unsigned int x) { cout << x << "\n"; }
void print(long long x) { cout << x << "\n"; }
void print(unsigned long long x) { cout << x << "\n"; }
void print(float x) { cout << x << "\n"; }
void print(double x) { cout << x << "\n"; }
void print(long double x) { cout << x << "\n"; }
void print(char x) { cout << x << "\n"; }
void print(const char *x) { cout << x << "\n"; }
void print(string x) { cout << x << "\n"; }
void print(bool x) { cout << x << "\n"; }
template <class T, class... Ts>
void print(T t, Ts... ts) {
  cout << t << " ";
  print(ts...);
}
template <typename T1, typename T2>
void print(pair<T1, T2> a) {
  print(a.first, a.second);
}
template <typename T>
void print(T a) {
  for (auto it : a) {
    print(it);
  }
}
template <class T, class... Ts>
void prine(T t, Ts... ts) {
  print(t, ts...);
  exit(0);
}
}  // namespace Output
using namespace Output;
const int dx[] = {1, -1, 0, 0};
const int dy[] = {0, 0, 1, -1};
const int INF = 1e9;
const long long INFL = 1e18;
const int MOD = 1e9 + 7;
const int N = 1e6 + 10;
long long dp[N];
pair<int, int> a[N];
int main() {
  setIO();
  int n, k;
  long long l;
  cin >> n >> l >> k;
  long long Q = l / n;
  long long r = l % n;
  for (int i = 0; i < n; i++) {
    cin >> a[i].first;
    a[i].second = i;
  }
  dp[0] = 1;
  sort(a, a + n);
  long long res = 0;
  for (int len = 0; len < k; len++) {
    if (len > Q) {
      break;
    }
    long long sum = 0;
    int pos = 0;
    for (int i = 0; i < n; i++) {
      while (pos < n && a[pos].first <= a[i].first) {
        sum += dp[pos++];
        sum %= MOD;
      }
      dp[i] = sum;
      res += (dp[i] * ((Q - len) % MOD)) % MOD;
      res %= MOD;
      if (a[i].second < r) {
        res += dp[i];
        res %= MOD;
      }
    }
  }
  print(res);
  return 0;
}

```