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;
const int MOD = 1e9 + 7;
struct matrix {
  int arr[208][208];
  matrix() { memset(arr, 0, sizeof(arr)); }
  int* operator[](int x) { return arr[x]; }
  friend matrix operator*(matrix p, matrix q) {
    matrix x;
    for (int i = 0; i < 208; ++i)
      for (int j = 0; j < 208; ++j)
        for (int k = 0; k < 208; ++k)
          x[i][k] = (x[i][k] + 1ll * p[i][j] * q[j][k]) % MOD;
    return x;
  }
} trs, F;
int N, K, M;
int main() {
  cin >> N >> K >> M;
  F[0][0] = 1;
  for (int i = 0; i <= K; ++i)
    for (int j = 0; j < 16; ++j) {
      trs[(i << 4) | j][(i << 4) | ((j & ~8) << 1)] = 1;
      if (i != K)
        trs[(i << 4) | j][((i + 1) << 4) | ((j & ~8) << 1 | 1)] =
            __builtin_popcount(j & ((1 << M) - 1)) + 1;
    }
  while (N) {
    if (N & 1) F = F * trs;
    trs = trs * trs;
    N >>= 1;
  }
  int sum = 0;
  for (int j = 0; j < 16; ++j) sum = (sum + F[0][K << 4 | j]) % MOD;
  cout << sum;
  return 0;
}
