Problem2931--Yet Another Number Sequence

2931: Yet Another Number Sequence

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

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

Source/Category

 
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