B'Santa has an infinite number of candies for each of m flavours. You are given a rooted tree with n vertices. The root of the tree is the vertex 1 . Each vertex contains exactly one candy. The i -th vertex has a candy of flavour f_i . Sometimes Santa fears that candies of flavour k have melted. He chooses any vertex x randomly and sends the subtree of x to the Bakers for a replacement. In a replacement, all the candies with flavour k are replaced with a new candy of the same flavour. The candies which are not of flavour k are left unchanged. After the replacement, the tree is restored. The actual cost of replacing one candy of flavour k is c_k (given for each k ). The Baker keeps the price fixed in order to make calculation simple. Every time when a subtree comes for a replacement, the Baker charges C , no matter which subtree it is and which flavour it is. Suppose that for a given flavour k the probability that Santa chooses a vertex for replacement is same for all the vertices. You need to find out the expected value of error in calculating the cost of replacement of flavour k . The error in calculating the cost is defined as follows. Error E(k) = (Actual Cost xe2 x80 x93 Price charged by the Bakers) ^ 2. Note that the actual cost is the cost of replacement of one candy of the flavour k multiplied by the number of candies in the subtree. Also, sometimes Santa may wish to replace a candy at vertex x with a candy of some flavour from his pocket. You need to handle two types of operations: The first line of the input contains four integers n ( 2 xe2 x80 x89 <= qslant xe2 x80 x89n xe2 x80 x89 <= qslant xe2 x80 x895 cdot 10^4 ), m , q , C ( 1 xe2 x80 x89 <= qslant xe2 x80 x89m, q xe2 x80 x89 <= qslant xe2 x80 x895 cdot 10^4 , 0 <= qslant C <= qslant 10^6 ) -- the number of nodes, total number of different flavours of candies, the number of queries and the price charged by the Bakers '...