#include <bits/stdc++.h>
using namespace std;
const int i = 1 << 21, p = 1000000007, n = 1000000;
int q, a[n], a1[n], f[i], h[n];
long long y, u;
void qs(int q, int w) {
  int e = q, r = w, t = h[q + (rand() % (w - q + 1))], y;
  do {
    while (h[e] < t) e++;
    while (h[r] > t) r--;
    if (e <= r) {
      y = h[e];
      h[e] = h[r];
      h[r] = y;
      e++;
      r--;
    }
  } while (e <= r);
  if (q < r) qs(q, r);
  if (e < w) qs(e, w);
}
int bp(int w) {
  int c, v, c1 = -1;
  for (v = i >> 2; v; v >>= 1) {
    c = c1 + v;
    if ((c < q) && (h[c] <= w)) c1 = c;
  }
  return c1;
}
int l(int e) {
  e = bp(e) + 1;
  int w = 1, r = 0, t;
  for (t = i >> 2; t; t >>= 1) {
    w <<= 1;
    if (e >= t) {
      e -= t;
      r += f[w];
      if (r >= p) r -= p;
      w++;
    }
  }
  return r;
}
void m(int w, int e) {
  for (w = bp(w) + (i >> 1); w; w >>= 1) {
    f[w] += e;
    if (f[w] >= p) f[w] -= p;
    if (f[w] < 0) f[w] += p;
  }
}
void del(int w) {
  for (w += i >> 1; w; w >>= 1) f[w] = 0;
}
int main() {
  long long ans = 0, c, v, y1, y2;
  int w, e, r, t;
  for (w = 0; w < i; w++) f[w] = 0;
  cin >> q >> y >> u;
  y1 = y % q;
  y2 = y / q;
  for (w = 0; w < q; w++) {
    scanf("%d", &a[w]);
    h[w] = a[w];
  }
  qs(0, q - 1);
  ans = y % p;
  for (w = 0; w < q; w++) m(a[w], 1);
  for (w = 1; w < u; w++) {
    if (w > y2) break;
    c = 0;
    for (e = 0; e < q; e++) {
      a1[e] = l(a[e]);
      c += a1[e];
    }
    for (e = 0; e < q; e++) del(e);
    for (e = 0; e < q; e++) m(a[e], a1[e]);
    c %= p;
    if (w + 1 <= y2) ans = (ans + c * ((y2 - w) % p)) % p;
    if ((y1 > 0)) {
      for (e = 0; e < y1; e++) {
        ans += a1[e];
      }
      ans %= p;
    }
    if (w + 1 > y2) break;
  }
  cout << ans;
  return 0;
}

### 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 int i = 1 << 21, p = 1000000007, n = 1000000;
int q, a[n], a1[n], f[i], h[n];
long long y, u;
void qs(int q, int w) {
  int e = q, r = w, t = h[q + (rand() % (w - q + 1))], y;
  do {
    while (h[e] < t) e++;
    while (h[r] > t) r--;
    if (e <= r) {
      y = h[e];
      h[e] = h[r];
      h[r] = y;
      e++;
      r--;
    }
  } while (e <= r);
  if (q < r) qs(q, r);
  if (e < w) qs(e, w);
}
int bp(int w) {
  int c, v, c1 = -1;
  for (v = i >> 2; v; v >>= 1) {
    c = c1 + v;
    if ((c < q) && (h[c] <= w)) c1 = c;
  }
  return c1;
}
int l(int e) {
  e = bp(e) + 1;
  int w = 1, r = 0, t;
  for (t = i >> 2; t; t >>= 1) {
    w <<= 1;
    if (e >= t) {
      e -= t;
      r += f[w];
      if (r >= p) r -= p;
      w++;
    }
  }
  return r;
}
void m(int w, int e) {
  for (w = bp(w) + (i >> 1); w; w >>= 1) {
    f[w] += e;
    if (f[w] >= p) f[w] -= p;
    if (f[w] < 0) f[w] += p;
  }
}
void del(int w) {
  for (w += i >> 1; w; w >>= 1) f[w] = 0;
}
int main() {
  long long ans = 0, c, v, y1, y2;
  int w, e, r, t;
  for (w = 0; w < i; w++) f[w] = 0;
  cin >> q >> y >> u;
  y1 = y % q;
  y2 = y / q;
  for (w = 0; w < q; w++) {
    scanf("%d", &a[w]);
    h[w] = a[w];
  }
  qs(0, q - 1);
  ans = y % p;
  for (w = 0; w < q; w++) m(a[w], 1);
  for (w = 1; w < u; w++) {
    if (w > y2) break;
    c = 0;
    for (e = 0; e < q; e++) {
      a1[e] = l(a[e]);
      c += a1[e];
    }
    for (e = 0; e < q; e++) del(e);
    for (e = 0; e < q; e++) m(a[e], a1[e]);
    c %= p;
    if (w + 1 <= y2) ans = (ans + c * ((y2 - w) % p)) % p;
    if ((y1 > 0)) {
      for (e = 0; e < y1; e++) {
        ans += a1[e];
      }
      ans %= p;
    }
    if (w + 1 > y2) break;
  }
  cout << ans;
  return 0;
}

```