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5773: Yet Another Number Sequence

内存限制：256 MB 时间限制：2 S
题面：传统 评测方式：文本比较 上传者：
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题目描述

C. Yet Another Number Sequence
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
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

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