Rikka with graph

As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:


A non-directed graph $G$ has no multiple edges and self loops. If every connected component of G has an Euler’s circuit, we call G perfect. Now Yuta wants to know the numbers of different perfect graphs which has $n$ vertices and no less than $m$ edges (In this problem, we think all the $n$ vertices are different from each other)


It is too difficult for Rikka. Can you help her?

This problem has multi test cases (no more than $100$). For each test case, The first line contains two numbers $n,m(1 \leq n \leq 10^{18}, 0 \leq m \leq 80)$.

For each test cases print only one number – the answer. The answer may be very large, so you only print is module $1e9+7$.

3 0
4 0

2
8

For the first case, there are two possible ways. First one is that there is no edge in the graph.
Second one is that there is a edge between every two distinct vertices.

BestCoder Round #37 ($)