Yet Another Number Sequence

1000ms

262144K

Description:

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

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

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

A_i(k) = F_i × i^k (i ≥ 1).

In this problem, your task is to calculate the following sum: A₁(k) + A₂(k) + ... + A_n(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 A_i(k) modulo 1000000007 (10⁹ + 7).

Sample Input:

1 1

Sample Output:

Sample Input:

4 1

Sample Output:

Sample Input:

5 2

Sample Output:

Sample Input:

7 4

Sample Output:

Informação

Provedor Codeforces

Código CF392C