B'There are N cities in the country of Numbata, numbered from 1 to N . Currently, there is no road connecting them. Therefore, each of these N cities proposes a road candidate to be constructed. City i likes to connect with city A_i , so city i proposes to add a direct bidirectional road connecting city i and city A_i . It is guaranteed that no two cities like to connect with each other. In other words, there is no pair of integers i and j where A_i = j and A_j = i . It is also guaranteed that any pair of cities are connected by a sequence of road proposals. In other words, if all proposed roads are constructed, then any pair of cities are connected by a sequence of constructed road. City i also prefers the road to be constructed using a specific material. Each material can be represented by an integer (for example, 0 for asphalt, 1 for wood, etc.). The material that can be used for the road connecting city i and city A_i is represented by an array B_i containing M_i integers: [(B_i)_1, (B_i)_2, ... , (B_i)_{M_i}] . This means that the road connecting city i and city A_i can be constructed with either of the material in B_i . There are K workers to construct the roads. Each worker is only familiar with one material, thus can only construct a road with a specific material. In particular, the i^{th} worker can only construct a road with material C_i . Each worker can only construct at most one road. You want to assign each worker to construct a road such that any pair of cities are connected by a sequence of constructed road. Input begins with a line containing two integers: N K ( 3 <= N <= 2000 ; 1 <= K <= 2000 ) representing the number of cities and the number of workers, respectively. The next N lines each contains several integers: A_i M_i (B_i)_1 , (B_'...