3350: Yet Another Number Sequence
金币值：2
定数：1
时间限制：2.000 s
内存限制：256 M
正确：0
提交：0
正确率：0.00% 命题人：
题目描述
time limit per test
1 secondmemory limit per test
256 megabytesinput
standard inputoutput
standard outputEveryone knows what the Fibonacci sequence is. This sequence can be defined by the recurrence relation:
We'll define a new number sequence Ai(k) by the formula:
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