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;
int n, m, K, S, cnt[1 << 4];
struct Mat {
  int s[225][225];
  Mat() { memset(s, 0, sizeof s); }
  Mat operator*(const Mat &B) {
    Mat ret;
    for (int k = S * (K + 1) - 1; k >= 0; k--)
      for (int i = S * (K + 1) - 1; i >= 0; i--)
        if (s[i][k])
          for (int j = S * (K + 1) - 1; j >= 0; j--)
            if (B.s[k][j])
              ret.s[i][j] = (ret.s[i][j] + 1ll * s[i][k] * B.s[k][j]) % mod;
    return ret;
  }
} f, g;
int main() {
  scanf("%d%d%d", &n, &K, &m), S = (1 << m);
  f.s[0][0] = 1;
  for (int i = 0; i < S; i++) cnt[i] = cnt[i >> 1] + (i & 1);
  for (int i = 0; i <= K; i++)
    for (int j = 0; j < S; j++) {
      g.s[i * S + j][i * S + ((j << 1) & (S - 1))]++;
      if (i < K)
        g.s[i * S + j][(i + 1) * S + ((j << 1 | 1) & (S - 1))] += cnt[j] + 1;
    }
  for (; n; n >>= 1, g = g * g)
    if (n & 1) f = f * g;
  int ans = 0;
  for (int i = 0; i < S; i++) ans = (ans + f.s[0][K * S + i]) % mod;
  printf("%d\n", ans);
}
