Description
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 modulo1000000007 (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).
Sample Input
Input
1 1Output
1Input
4 1Output
34Input
5 2Output
316Input
7 4Output
73825
【分析】 哈哈照着上一题的方法我就弄出来了~~ 应该是形如 x^k的形式,x很大,k较小的时候可以用二项式定理展开,求递推式然后矩阵加速。。
时间: 2024-07-31 23:29:24