You are given a tree with (n) vertices numbered from (1) to (n). A slime occupies exactly (m) vertices of the tree. It is guaranteed that the subgraph induced by the occupied vertices is connected. Initially, the slime occupies vertices (s_1,s_2,\ldots,s_m). First, we define a function (f) on a sequence of vertices. Consider a sequence (a_1,a_2,\ldots,a_k). There are (k) pieces of food. For each (i), the (i)-th piece of food is located at vertex (a_i). At first, only the first piece of food appears. The slime may perform the following operations any number of times: Move . The slime removes itself from one currently occupied vertex and expands to one currently unoccupied vertex. Formally, let (S) be the current set of occupied vertices. Choose a vertex (u\in S) and a vertex (v\notin S), and replace (S) with ((S\setminus{u})\cup{v}). After the operation, the subgraph induced by (S) must still be connected. Formally, let (S) be the current set of occupied vertices. Choose a vertex (u\in S) and a vertex (v\notin S), and replace (S) with ((S\setminus{u})\cup{v}). After the operation, the subgraph induced by (S) must still be connected. Eat . If the (i)-th piece of food has appeared and the slime currently occupies vertex (a_i), then the slime may eat the (i)-th piece of food. If (1\le i \lt k), the ((i+1))-th piece of food appears immediately after that. Eating does not change the occupied vertices. Define (f(a_1,a_2,\ldots,a_k)) as the minimum number of Move operations needed for the slime to eat all (k) pieces of food in order, starting from the initial occupied vertices (s_1,s_2,\ldots,s_m). There are (q) queries. The input is forced online. The input gives encoded values (p_1,p_2,\ldots,p_q). Let (\mathrm{ans}_0=0). For each (i=1,2,\ldots,q), the actual vertex of the (i)-th query is $$$c_i=((p_i-1+\mathrm{ans}_{i