SP11834 DOJ2 - DOJO Corridor II

There's a 5×N rectangular corridor in the hall's dojo, one place is already taken by a magic hanjō (1×1 square). You have to put tatamis (1×2 rectangle) in order to cover exactly the rest of the corridor. Sometimes it's possible, sometimes not!

The input begins with the number T of test cases in a single line. In each of the next T lines there are an integer N the H-length of the corridor, and I, J the coordinates of the magic hanjō. See sample input for details format.

For each test case, print the number of possibility to do the job, modulo 1000000007.