Problem #191
Save Jon Snow
Jon Snow hands Gendry a message, tells him to go to Eastwatch and send a raven to Daenerys to rescue them. Currently, Gendry is at (0,0) and the castle is situated at (N,N). In order to escape the battlefield, he can only move from (i,j) to (i,j+1) or (i+1,j) or (i+1,j+1).
Find the number of paths that can be taken by Gendry to reach the castle modulo 10^9+7 for N = 10^7.