386. Happy Birthday, Jedi Knight!

Time limit per test: 0.25 second(s)
Memory limit: 262144 kilobytes
input: standard
output: standard

Jedi Knight has sneaked into the new model of Death Star. He is searching for very important enemy documents. For each document he finds he will get a certain amount of money from the Jedi Council. A new model of Death Star has the form of an n-dimensional parallelepiped. Its edges are parallel to vectors v1,..., vn with integer coordinates and have the lengths equal to lengths of the corresponding vectors. There is one document located in every integer point inside or on the border of the Death Star. If for any k (0 ≤ kn) a document is inside some k-dimensional facet of the parallelepiped, but either k = 0 or it is not inside any (k-1)-dimensional facet, then its price is 2k. Your task is to calculate the total amount of money Jedi can earn if he gets all the documents on the Death Star. The answer can be enormous, but Jedi isn't afraid of this fact, so you should output it modulo prime number p.
Input
The first line of the input file contains numbers n and p (2 ≤ n ≤ 50, ). The next n lines contain description of vectors vi. Each of these lines contains n integer numbers aij (0 ≤ aijp-1) — coordinates of the vector vi. It is guaranteed that these vectors are linearly independent.
Output
Output must contain one number — the answer modulo p.
Example(s)
sample input
sample output
2 43
1 0
0 1
4


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