There are \(2n\) students in a school. Calculate the number of ways pick a group of at least 2 students so that for pair of
students a and b in this group, \(|a − b| \ne 1\) and \(|a − b| \ne n + x\).

Input

• The first line of input contains 2 integers \(n\) and \(x (1 \le n \le 10^{18}, 0 \le x \le n)\).

Output

• Output a single integer, the answer to the problem modulo \(10^9 + 7\).

Example

2 1

2