Problem: Everyone knows what the Fibonacci sequence is. This sequence can be defined by the recurrence relation: 

F1 = 1, F2 = 2, Fi = Fi - 1 + Fi - 2 (i > 2).

We'll define a new number sequence Ai(k) by the formula: 

Ai(k) = Fi × ik (i ≥ 1).

In this problem, your task is to calculate the following sum: A1(k) + A2(k) + ... + An(k). The answer can be very large, so print it modulo 1000000007 (109 + 7).

Input

The first line contains two space-separated integers n, k (1 ≤ n ≤ 1017; 1 ≤ k ≤ 40).

Output

Print a single integer — the sum of the first n elements of the sequence Ai(k) modulo 1000000007 (109 + 7).

Examples

Input

1 1


Output

1


Input

4 1


Output

34


Input

5 2


Output

316


Input

7 4


Output

73825

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long t, n, k;
long long tot;
const long long mod = 1e9 + 7;
struct matrix {
  long long mp[91][91] = {};
  void zero() {
    for (long long i = 1; i <= tot; i++)
      for (long long j = 1; j <= tot; j++) mp[i][j] = 0;
  }
};
matrix operator*(matrix x, matrix y) {
  matrix ans;
  for (long long i = 1; i <= tot; i++)
    for (long long j = 1; j <= tot; j++)
      for (long long k = 1; k <= tot; k++)
        ans.mp[i][j] += x.mp[i][k] * y.mp[k][j] % mod, ans.mp[i][j] %= mod;
  return ans;
}
long long c[91][91];
int main() {
  for (long long i = 1; i <= 90; i++) {
    c[i][1] = c[i][i] = 1;
    for (long long j = 2; j <= i - 1; j++)
      c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % mod;
  }
  scanf("%lld%lld", &n, &k);
  n--;
  tot = k * 2 + 3;
  matrix res, ans;
  res.mp[1][1] = 1;
  for (long long i = 1; i <= k + 1; i++)
    for (long long j = 1; j <= k + 1; j++)
      res.mp[i + 1][j + 1] = res.mp[i + 1][j + k + 2] =
          res.mp[i + k + 2][j + 1] = res.mp[1][j + 1] = res.mp[1][j + k + 2] =
              c[i][j];
  for (long long i = 1; i <= tot; i++) ans.mp[i][i] = 1;
  while (n) {
    if (n & 1) ans = ans * res;
    res = res * res;
    n >>= 1;
  }
  long long anss = 0;
  for (long long i = 1; i <= tot; i++) anss += ans.mp[1][i], anss %= mod;
  printf("%lld", anss);
}