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;
const int N = 100;
const int Mo = 1e9 + 7;
long long n, m;
int k;
long long c[N][N];
struct Martix {
  long long a[N][N];
  Martix() { memset(a, 0, sizeof(a)); }
} base;
Martix Mul(Martix a, Martix b) {
  Martix res;
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j)
      for (int k = 0; k < n; ++k) {
        res.a[i][j] += a.a[i][k] * b.a[k][j];
        res.a[i][j] %= Mo;
      }
  return res;
}
Martix Pow(Martix a, long long t) {
  Martix res;
  for (int i = 0; i < n; ++i) res.a[i][i] = 1;
  while (t) {
    if (t & 1) res = Mul(res, a);
    a = Mul(a, a);
    t >>= 1;
  }
  return res;
}
void Init() {
  scanf("%I64d%d", &m, &k);
  n = 2 * k + 3;
  memset(c, 0, sizeof(c));
  for (int i = 0; i <= k; ++i) {
    c[i][0] = c[i][i] = 1;
    for (int j = 1; j < i; ++j) c[i][j] = c[i - 1][j - 1] + c[i - 1][j];
  }
}
void Work() {
  if (m == 1) {
    puts("1");
    return;
  }
  for (int i = 0; i <= k; ++i)
    for (int j = 0; j <= i; ++j)
      base.a[i][j] = base.a[i + k + 1][j] = base.a[i][j + k + 1] = c[i][j];
  base.a[n - 1][k] = base.a[n - 1][n - 1] = 1;
  Martix res = Pow(base, m);
  long long ans = 0;
  for (int i = 0; i < 2 * k + 2; i++) ans = (ans + res.a[n - 1][i]) % Mo;
  printf("%I64d\n", ans);
}
int main() {
  Init();
  Work();
  return 0;
}