#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
long long n, k, l, a[1000010], m, p, q, b[1000010], d, c[1000010], f[1000010],
    g[1000010], ans;
struct BIT {
  long long a[1000010];
  void clear() { memset(a, 0, sizeof(a)); }
  void add(int x, long long v) {
    for (; x <= 1000010 - 5; x += x & (-x)) a[x] = (a[x] + v + mod) % mod;
  }
  long long get(int x) {
    long long ans = 0;
    for (; x; x -= x & (-x)) ans = (ans + a[x]) % mod;
    return ans;
  }
} tr;
int main() {
  scanf("%lld%lld%lld", &n, &l, &k);
  for (int i = 1; i <= n; i++) scanf("%lld", &a[i]), b[i] = a[i];
  sort(b + 1, b + n + 1);
  d = unique(b + 1, b + n + 1) - b - 1;
  for (int i = 1; i <= n; i++) a[i] = lower_bound(b + 1, b + d + 1, a[i]) - b;
  m = l / n;
  p = l % n;
  if (!p) {
    m--;
    p += n;
  }
  q = max(0ll, m - k + 1);
  q %= mod;
  int cnt = 0;
  for (int i = 1; i <= k - 1; i++)
    for (int j = 1; j <= n; j++) c[++cnt] = a[j];
  for (int i = 1; i <= p; i++) c[++cnt] = a[i];
  for (int i = cnt - p + 1; i <= cnt; i++) f[i] = 1, tr.add(c[i], f[i]);
  for (int i = k - 1; i; --i) {
    for (int j = 1; j <= n; j++) {
      int pos = (i - 1) * n + j;
      f[pos] = (tr.get(1000010 - 5) - tr.get(c[pos] - 1) + mod) % mod;
    }
    for (int j = 1; j <= n; j++) {
      int pos = (i - 1) * n + j;
      if (pos + n <= cnt) tr.add(c[pos + n], -f[pos + n]);
      tr.add(c[pos], f[pos]);
    }
  }
  for (int i = max(cnt - p - m * n + 1, 1ll); i <= cnt; i++)
    ans = (ans + f[i]) % mod;
  memset(c, 0, sizeof(c));
  tr.clear();
  cnt = 0;
  for (int i = 1; i <= k; i++)
    for (int j = 1; j <= n; j++) c[++cnt] = a[j];
  for (int i = cnt - n + 1; i <= cnt; i++) g[i] = 1, tr.add(c[i], g[i]);
  for (int i = k - 1; i; --i) {
    for (int j = 1; j <= n; j++) {
      int pos = (i - 1) * n + j;
      g[pos] = (tr.get(1000010 - 5) - tr.get(c[pos] - 1) + mod) % mod;
    }
    for (int j = 1; j <= n; j++) {
      int pos = (i - 1) * n + j;
      tr.add(c[pos + n], -g[pos + n]);
      tr.add(c[pos], g[pos]);
    }
  }
  long long tmp = 0;
  for (int i = 1; i <= min(m, k - 1); i++) {
    for (int j = 1; j <= n; j++) {
      int pos = (k - i) * n + j;
      tmp = (tmp + g[pos]) % mod;
    }
    ans = (ans + tmp) % mod;
  }
  tmp = 0;
  for (int i = 1; i <= k; i++)
    for (int j = 1; j <= n; j++) {
      int pos = (i - 1) * n + j;
      tmp = (tmp + g[pos]) % mod;
    }
  tmp = tmp * q % mod;
  ans = (ans + tmp) % mod;
  printf("%lld\n", ans);
  return 0;
}

### Prompt

Create a solution in CPP for 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 n, k, l, a[1000010], m, p, q, b[1000010], d, c[1000010], f[1000010],
    g[1000010], ans;
struct BIT {
  long long a[1000010];
  void clear() { memset(a, 0, sizeof(a)); }
  void add(int x, long long v) {
    for (; x <= 1000010 - 5; x += x & (-x)) a[x] = (a[x] + v + mod) % mod;
  }
  long long get(int x) {
    long long ans = 0;
    for (; x; x -= x & (-x)) ans = (ans + a[x]) % mod;
    return ans;
  }
} tr;
int main() {
  scanf("%lld%lld%lld", &n, &l, &k);
  for (int i = 1; i <= n; i++) scanf("%lld", &a[i]), b[i] = a[i];
  sort(b + 1, b + n + 1);
  d = unique(b + 1, b + n + 1) - b - 1;
  for (int i = 1; i <= n; i++) a[i] = lower_bound(b + 1, b + d + 1, a[i]) - b;
  m = l / n;
  p = l % n;
  if (!p) {
    m--;
    p += n;
  }
  q = max(0ll, m - k + 1);
  q %= mod;
  int cnt = 0;
  for (int i = 1; i <= k - 1; i++)
    for (int j = 1; j <= n; j++) c[++cnt] = a[j];
  for (int i = 1; i <= p; i++) c[++cnt] = a[i];
  for (int i = cnt - p + 1; i <= cnt; i++) f[i] = 1, tr.add(c[i], f[i]);
  for (int i = k - 1; i; --i) {
    for (int j = 1; j <= n; j++) {
      int pos = (i - 1) * n + j;
      f[pos] = (tr.get(1000010 - 5) - tr.get(c[pos] - 1) + mod) % mod;
    }
    for (int j = 1; j <= n; j++) {
      int pos = (i - 1) * n + j;
      if (pos + n <= cnt) tr.add(c[pos + n], -f[pos + n]);
      tr.add(c[pos], f[pos]);
    }
  }
  for (int i = max(cnt - p - m * n + 1, 1ll); i <= cnt; i++)
    ans = (ans + f[i]) % mod;
  memset(c, 0, sizeof(c));
  tr.clear();
  cnt = 0;
  for (int i = 1; i <= k; i++)
    for (int j = 1; j <= n; j++) c[++cnt] = a[j];
  for (int i = cnt - n + 1; i <= cnt; i++) g[i] = 1, tr.add(c[i], g[i]);
  for (int i = k - 1; i; --i) {
    for (int j = 1; j <= n; j++) {
      int pos = (i - 1) * n + j;
      g[pos] = (tr.get(1000010 - 5) - tr.get(c[pos] - 1) + mod) % mod;
    }
    for (int j = 1; j <= n; j++) {
      int pos = (i - 1) * n + j;
      tr.add(c[pos + n], -g[pos + n]);
      tr.add(c[pos], g[pos]);
    }
  }
  long long tmp = 0;
  for (int i = 1; i <= min(m, k - 1); i++) {
    for (int j = 1; j <= n; j++) {
      int pos = (k - i) * n + j;
      tmp = (tmp + g[pos]) % mod;
    }
    ans = (ans + tmp) % mod;
  }
  tmp = 0;
  for (int i = 1; i <= k; i++)
    for (int j = 1; j <= n; j++) {
      int pos = (i - 1) * n + j;
      tmp = (tmp + g[pos]) % mod;
    }
  tmp = tmp * q % mod;
  ans = (ans + tmp) % mod;
  printf("%lld\n", ans);
  return 0;
}

```