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).