Codeforces Round #416 (Div. 2) has been moved to start on 27.05.2017 09:35 (UTC). ×

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