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 maxn = 1e5 + 100;
const int maxk = 12 + 2;
const int maxmask = (1 << 4) + 5;
const int mod = 1e9 + 7;
inline void add(int &target, int val) { (target += val) %= mod; }
int n, K, m;
int dp[maxn][maxmask][maxk];
map<pair<int, int>, int> comp_mem;
map<int, pair<int, int> > decmp_mem;
int comp(int k, int mask) {
  auto key = make_pair(k, mask);
  if (comp_mem.count(key)) return comp_mem[key];
  int sz = comp_mem.size();
  comp_mem[key] = sz;
  decmp_mem[sz] = key;
  return sz;
}
vector<vector<int> > create_zero(int sz) {
  vector<vector<int> > res(sz, vector<int>(0));
  for (int i = 0; i < sz; i++) {
    res[i].resize(sz);
    for (int j = 0; j < sz; j++) {
      res[i][j] = 0;
    }
  }
  return res;
}
vector<vector<int> > create_eye(int sz) {
  vector<vector<int> > res(sz, vector<int>(0));
  for (int i = 0; i < sz; i++) {
    res[i].resize(sz);
    for (int j = 0; j < sz; j++) {
      res[i][j] = 0;
    }
    res[i][i] = 1;
  }
  return res;
}
vector<vector<int> > operator*(const vector<vector<int> > &x,
                               const vector<vector<int> > &y) {
  assert(x[0].size() == y.size());
  int sz = x.size();
  vector<vector<int> > res = create_zero(sz);
  for (int i = 0; i < sz; i++) {
    for (int j = 0; j < sz; j++) {
      for (int k = 0; k < sz; k++) {
        add(res[i][j], 1ll * x[i][k] * y[k][j] % mod);
      }
    }
  }
  return res;
}
vector<vector<int> > powmod(vector<vector<int> > x, int y) {
  vector<vector<int> > res = create_eye(x.size());
  while (y) {
    if (y & 1) {
      res = res * x;
    }
    y >>= 1;
    x = x * x;
  }
  return res;
}
void add_trans(vector<vector<int> > &trans, int x, int y, int s) {
  trans[y][x] += s;
}
void debug(vector<vector<int> > x) {
  for (auto row : x) {
    for (auto item : row) {
      cout << item << " ";
    }
    cout << endl;
  }
}
int main() {
  auto start_ = clock();
  scanf("%d%d%d", &n, &K, &m);
  for (int k = 0; k <= K; k++) {
    for (int mask = 0; mask < (1 << m); mask++) {
      comp(k, mask);
    }
  }
  int SZ = (K + 1) * (1 << m);
  cerr << SZ << endl;
  vector<vector<int> > trans = create_zero(SZ);
  for (int mask = 0; mask < (1 << m); mask++) {
    for (int k = 0; k <= K; k++) {
      add_trans(trans, comp(k, mask), comp(k, mask >> 1), 1);
      if (k == K) continue;
      add_trans(trans, comp(k, mask), comp(k + 1, (mask >> 1) | (1 << (m - 1))),
                1 + __builtin_popcount(mask));
    }
  }
  vector<vector<int> > final_trans = powmod(trans, n);
  int col_id = comp(0, 0);
  int ans = 0;
  for (int mask = 0; mask < (1 << m); mask++) {
    int k = K;
    int row_id = comp(k, mask);
    add(ans, final_trans[row_id][col_id]);
  }
  cout << ans << endl;
  auto end_ = clock();
  cerr << "runtime: " << end_ - start_ << endl;
  return 0;
}
