This problem is same as the previous one, but has larger constraints.

Aki is playing a new video game. In the video game, he will control Neko, the giant cat, to fly between planets in the Catniverse.

There are n planets in the Catniverse, numbered from 1 to n. At the beginning of the game, Aki chooses the planet where Neko is initially located. Then Aki performs k - 1 moves, where in each move Neko is moved from the current planet x to some other planet y such that:

  * Planet y is not visited yet. 
  * 1 ≤ y ≤ x + m (where m is a fixed constant given in the input) 



This way, Neko will visit exactly k different planets. Two ways of visiting planets are called different if there is some index i such that, the i-th planet visited in the first way is different from the i-th planet visited in the second way.

What is the total number of ways to visit k planets this way? Since the answer can be quite large, print it modulo 10^9 + 7.

Input

The only line contains three integers n, k and m (1 ≤ n ≤ 10^9, 1 ≤ k ≤ min(n, 12), 1 ≤ m ≤ 4) — the number of planets in the Catniverse, the number of planets Neko needs to visit and the said constant m.

Output

Print exactly one integer — the number of different ways Neko can visit exactly k planets. Since the answer can be quite large, print it modulo 10^9 + 7.

Examples

Input


3 3 1


Output


4


Input


4 2 1


Output


9


Input


5 5 4


Output


120


Input


100 1 2


Output


100

Note

In the first example, there are 4 ways Neko can visit all the planets:

  * 1 → 2 → 3 
  * 2 → 3 → 1 
  * 3 → 1 → 2 
  * 3 → 2 → 1 



In the second example, there are 9 ways Neko can visit exactly 2 planets:

  * 1 → 2 
  * 2 → 1 
  * 2 → 3 
  * 3 → 1 
  * 3 → 2 
  * 3 → 4 
  * 4 → 1 
  * 4 → 2 
  * 4 → 3 



In the third example, with m = 4, Neko can visit all the planets in any order, so there are 5! = 120 ways Neko can visit all the planets.

In the fourth example, Neko only visit exactly 1 planet (which is also the planet he initially located), and there are 100 ways to choose the starting planet for Neko.
#include <bits/stdc++.h>
using namespace std;
inline int read() {
  register int x = 0, f = 1;
  register char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = 0;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + (ch ^ '0');
    ch = getchar();
  }
  return f ? x : -x;
}
const int _ = 13 * 16 + 1, mod = 1e9 + 7;
int n, k, m, N, id[13][16], cnt[1 << 4];
inline void inc(int &x, int y) { x = x + y < mod ? x + y : x + y - mod; }
struct matrix {
  int x[_][_];
  inline matrix() { memset(x, 0, sizeof x); }
  inline int *operator[](const int &p) { return x[p]; }
  inline const int *operator[](const int &p) const { return x[p]; }
  matrix operator*(const matrix &t) {
    matrix res;
    for (int k = (1), _ed = (N); k <= _ed; ++k)
      for (int i = (1), _ed = (N); i <= _ed; ++i)
        for (int j = (1), _ed = (N); j <= _ed; ++j)
          inc(res[i][j], 1ll * x[i][k] * t[k][j] % mod);
    return res;
  }
} a, t;
int main() {
  n = read(), k = read(), m = read();
  for (int i = (1), _ed = ((1 << m) - 1); i <= _ed; ++i)
    cnt[i] = cnt[i >> 1] + (i & 1);
  for (int i = (0), _ed = (k); i <= _ed; ++i)
    for (int j = (0), _ed = ((1 << m) - 1); j <= _ed; ++j) id[i][j] = ++N;
  a[1][1] = 1;
  for (int i = (0), _ed = (k); i <= _ed; ++i)
    for (int j = (0), _ed = ((1 << m) - 1); j <= _ed; ++j) {
      int s = (j << 1) & ((1 << m) - 1);
      inc(t[id[i][j]][id[i][s]], 1);
      if (i < k) inc(t[id[i][j]][id[i + 1][s | 1]], cnt[j] + 1);
    }
  for (; n; n >>= 1, t = t * t)
    if (n & 1) a = a * t;
  int ans = 0;
  for (int i = (0), _ed = ((1 << m) - 1); i <= _ed; ++i)
    inc(ans, a[1][id[k][i]]);
  printf("%d\n", ans);
  return 0;
}
