#include <bits/stdc++.h>
using namespace std;
const int mod = 1000000007;
const int Maxn = 1000005;
int a[Maxn];
int sum[Maxn];
int buff[Maxn];
int loc[Maxn], locc[Maxn];
vector<vector<int> > dp;
bool cmp(pair<int, int> X, pair<int, int> Y) { return X.first < Y.first; }
int main() {
  int n, k;
  long long l;
  scanf("%d %I64d %d", &n, &l, &k);
  dp.resize(k + 1);
  for (int i = 0; i <= k; i++) {
    dp[i].resize(n + 1);
  }
  for (int i = 1; i <= n; i++) {
    scanf("%d", &buff[i]);
    a[i] = buff[i];
  }
  sort(a + 1, a + 1 + n);
  dp[0][1] = 1;
  for (int i = 1; i <= n; i++) {
    loc[i] = upper_bound(a + 1, a + 1 + n, a[i]) - a - 1;
    locc[i] = upper_bound(a + 1, a + 1 + n, buff[i]) - a - 1;
  }
  for (int i = 1; i <= k; i++) {
    for (int j = 1; j <= n; j++) {
      sum[j] = sum[j - 1] + dp[i - 1][j];
      sum[j] %= mod;
    }
    for (int j = 1; j <= n; j++) {
      dp[i][j] = sum[loc[j]];
    }
  }
  long long res = 0;
  long long piece = l / (long long)n;
  long long rem = l % (long long)n;
  if (piece >= k) {
    long long sb = piece % mod;
    sb %= mod;
    for (int i = 1; i <= k; i++) {
      for (int j = 1; j <= n; j++) {
        res = (res + dp[i][j] * ((sb - i + 1 + mod) % mod) % mod) % mod;
      }
    }
    for (int j = 1; j <= rem; j++) {
      for (int i = 1; i <= k; i++) {
        res = (res + dp[i][locc[j]]) % mod;
      }
    }
    printf("%I64d\n", res);
  } else {
    long long sb = piece % mod;
    sb %= mod;
    for (int i = 1; i <= piece; i++) {
      for (int j = 1; j <= n; j++) {
        res = (res + dp[i][j] * ((sb - i + 1 + mod) % mod) % mod) % mod;
      }
    }
    for (int j = 1; j <= rem; j++) {
      for (int i = 1; i <= piece + 1; i++) {
        res = (res + dp[i][locc[j]]) % mod;
      }
    }
    printf("%I64d\n", res);
  }
  return 0;
}

### 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;
const int mod = 1000000007;
const int Maxn = 1000005;
int a[Maxn];
int sum[Maxn];
int buff[Maxn];
int loc[Maxn], locc[Maxn];
vector<vector<int> > dp;
bool cmp(pair<int, int> X, pair<int, int> Y) { return X.first < Y.first; }
int main() {
  int n, k;
  long long l;
  scanf("%d %I64d %d", &n, &l, &k);
  dp.resize(k + 1);
  for (int i = 0; i <= k; i++) {
    dp[i].resize(n + 1);
  }
  for (int i = 1; i <= n; i++) {
    scanf("%d", &buff[i]);
    a[i] = buff[i];
  }
  sort(a + 1, a + 1 + n);
  dp[0][1] = 1;
  for (int i = 1; i <= n; i++) {
    loc[i] = upper_bound(a + 1, a + 1 + n, a[i]) - a - 1;
    locc[i] = upper_bound(a + 1, a + 1 + n, buff[i]) - a - 1;
  }
  for (int i = 1; i <= k; i++) {
    for (int j = 1; j <= n; j++) {
      sum[j] = sum[j - 1] + dp[i - 1][j];
      sum[j] %= mod;
    }
    for (int j = 1; j <= n; j++) {
      dp[i][j] = sum[loc[j]];
    }
  }
  long long res = 0;
  long long piece = l / (long long)n;
  long long rem = l % (long long)n;
  if (piece >= k) {
    long long sb = piece % mod;
    sb %= mod;
    for (int i = 1; i <= k; i++) {
      for (int j = 1; j <= n; j++) {
        res = (res + dp[i][j] * ((sb - i + 1 + mod) % mod) % mod) % mod;
      }
    }
    for (int j = 1; j <= rem; j++) {
      for (int i = 1; i <= k; i++) {
        res = (res + dp[i][locc[j]]) % mod;
      }
    }
    printf("%I64d\n", res);
  } else {
    long long sb = piece % mod;
    sb %= mod;
    for (int i = 1; i <= piece; i++) {
      for (int j = 1; j <= n; j++) {
        res = (res + dp[i][j] * ((sb - i + 1 + mod) % mod) % mod) % mod;
      }
    }
    for (int j = 1; j <= rem; j++) {
      for (int i = 1; i <= piece + 1; i++) {
        res = (res + dp[i][locc[j]]) % mod;
      }
    }
    printf("%I64d\n", res);
  }
  return 0;
}

```