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>
long long n, k, m, cnt;
long long id[15][20];
struct matrix {
  long long c[210][210];
  matrix() { memset(c, 0, sizeof(c)); }
  matrix operator*(matrix &v) {
    matrix ans;
    for (long long i = 1; i <= cnt; i++)
      for (long long j = 1; j <= cnt; j++)
        for (long long k = 1; k <= cnt; k++)
          ans[i][j] = (ans[i][j] + c[i][k] * v[k][j] % 1000000007) % 1000000007;
    return ans;
  }
  long long *operator[](long long x) { return c[x]; }
} g, f;
signed main() {
  scanf("%lld %lld %lld", &n, &k, &m);
  for (long long i = 0; i <= k; i++)
    for (long long j = 0; j < (1 << m); j++) id[i][j] = ++cnt;
  for (long long i = 0; i <= k; i++)
    for (long long s = 0; s < (1 << m); s++) {
      long long t = s << 1 & ((1 << m) - 1);
      (g[id[i][s]][id[i][t]] += 1) %= 1000000007;
      if (i < k)
        (g[id[i][s]][id[i + 1][t | 1]] += __builtin_popcount(s) + 1) %=
            1000000007;
    }
  f[1][1] = 1;
  while (n) {
    if (n & 1) f = f * g;
    g = g * g;
    n >>= 1;
  }
  long long ret = 0;
  for (long long i = 0; i < (1 << m); i++)
    ret = (ret + f[1][id[k][i]]) % 1000000007;
  printf("%lld\n", ret);
  return 0;
}
