Problem Description

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?

Input

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

Output

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

Hint

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.