CF916E Jamie and Tree

To your surprise, Jamie is the final boss! Ehehehe. Jamie has given you a tree with $ n $ vertices, numbered from $ 1 $ to $ n $ . Initially, the root of the tree is the vertex with number $ 1 $ . Also, each vertex has a value on it. Jamie also gives you three types of queries on the tree: $ 1\ v $ — Change the tree's root to vertex with number $ v $ . $ 2\ u\ v\ x $ — For each vertex in the subtree of smallest size that contains $ u $ and $ v $ , add $ x $ to its value. $ 3\ v $ — Find sum of values of vertices in the subtree of vertex with number $ v $ . A subtree of vertex $ v $ is a set of vertices such that $ v $ lies on shortest path from this vertex to root of the tree. Pay attention that subtree of a vertex can change after changing the tree's root. Show your strength in programming to Jamie by performing the queries accurately!

The first line of input contains two space-separated integers $ n $ and $ q $ ( $ 1

For each query of the third type, output the required answer. It is guaranteed that at least one query of the third type is given by Jamie.

The following picture shows how the tree varies after the queries in the first sample.