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,..., v_n 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 ≤ k ≤ n) 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 2^k. 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.
The first line of the input file contains numbers n and p (2 ≤ n ≤ 50, ). The next n lines contain description of vectors v_i. Each of these lines contains n integer numbers a_ij (0 ≤ a_ij ≤ p-1) — coordinates of the vector v_i. It is guaranteed that these vectors are linearly independent.
Output must contain one number — the answer modulo p.

sample input	sample output
2 43 1 0 0 1	4