CodeForces - 392C Yet Another Number Sequence （二项式展开+矩阵加速）

Posted 2020-08-10 konjak魔芋

Yet Another Number Sequence

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 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 A_i(k) modulo 1000000007 (10⁹ + 7).

Sample Input

Input

1 1

Output

1

Input

4 1

Output

34

Input

5 2

Output

316

Input

7 4

Output

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。。