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;
const int maxn = 233;
int MOD(const int& x) { return x >= mod ? x - mod : x; }
int MOD(const int& x, const int& y) { return 1ll * x * y % mod; }
struct MAT {
  int v[maxn][maxn];
  MAT() { memset(v, 0, sizeof v); }
  int* operator[](int x) { return v[x]; }
  MAT operator*(MAT a) {
    MAT ret;
    for (int k = 0; k < maxn; ++k)
      for (int t = 0; t < maxn; ++t)
        for (int i = 0; i < maxn; ++i)
          ret[t][i] = MOD(ret[t][i] + MOD(v[t][k], a[k][i]));
    return ret;
  }
} b, ret;
int n, k, m, ans;
int main() {
  cin >> n >> k >> m;
  ret[0][0] = 1;
  for (int t = 0; t <= k; ++t)
    for (int i = 0; i < 16; ++i) {
      b[(t << 4) | i][(t << 4) | ((i & ~8) << 1)] = 1;
      if (t != k)
        b[(t << 4) | i][((t + 1) << 4) | ((i & ~8) << 1 | 1)] =
            __builtin_popcount(i & ((1 << m) - 1)) + 1;
    }
  for (int t = n; t; t >>= 1, b = b * b)
    if (t & 1) ret = ret * b;
  for (int t = 0; t < 16; ++t) ans = (ans + ret[0][k << 4 | t]) % mod;
  cout << ans << endl;
  return 0;
}
