TRKNIGHT  Travelling Knight
Your task is simple. A knight is placed on the top left corner of a chessboard having 2n rows and 2n columns. In how many ways can it move such that it ends up at a corner after atmost K moves ?
Input
The first line contains T the number of test cases. Each of the next T lines contain 2 integers : n,k
Output
Output T lines, one for each test case, containing the required total number of configurations. Since the answers can get very big, output the answer modulo 1000007.
Example
Sample Input :
3
2 1
2 2
3 3
Sample Output :
1
5
7
Constraints
1 <= T <= 20
2 <= n <= 12
1 <= k <= 1000000000
Added by:  Varun Jalan 
Date:  20100125 
Time limit:  0.839s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel Pentium G860 3GHz) 
Languages:  All except: NODEJS objc PERL 6 VB.net 
Resource:  own problem used for Codechef Snackdown Onsite 
hide comments
Francky:
20140529 16:18:36
Python3 validator (by Francky) : OK ;)


Hagen von Eitzen:
20110629 21:21:06
@ukasuevoli: don't forget the move sequence of length 0<k that simply stays in the initial corner 

ulasuevoli:
20110628 12:38:23
@varun ! How the answer for second case =5 ?


~ adieus ~:
20100201 08:12:40
need some hints ... should it be done with (A.M.)^K ? 

[Retired] Blue.Mary:
20100131 05:11:46
Er, seems that it needs ~6 seconds on my PC for only one test case if multiplying 150 size matrices... 

Ivan Katanic:
20100130 11:04:53
maybe you're right, it just seemed to me that it can be solved with fft...btw, multiplying 150 size matrices isn't enough? Last edit: 20100130 11:05:19 

Varun Jalan:
20100130 05:11:48
yes, in fact I do not know how to do it using FFT :D 

Ivan Katanic:
20100128 15:51:44
is that problem solvable without using FFT and such things(yes/no)? or that is the only way... 