I've encountered some interesting problems but I couldn't solve them. I really need some help.

First problem is: Given 3 integers N, M, X (1 <= N, M <= 10⁵, 1 <= X <= M). Calculate the number of ways to create N segments [L₁, R₁], [L₂, R₂], …, [L_N, R_N] (Li <= Hi) such that they satisfy two conditions:

• there is no i and k (i != k) that L_i <= L_k <= H_k <= H_i
• There is at least one segment which has L_i = X

Two ways are different if there exists j such that segment j in two ways are different.

Second problem is: Given a tree with 4 nodes 1, 2, 3 and 4. Node 1 is root. Nodes 2, 3 and 4 are leaf nodes. Diameter of the tree is the longest path on the tree. We have Q queries (1 <= Q <= 5 * 10⁵). For each query, we are given a leaf node v (1 <= v <= N, N is the number of nodes in the tree). Then we add two new nodes N + 1 and N + 2 to the tree, create two edges (v, N + 1) and (v, N + 2). Output after each query is the diameter of the tree.

Thanks in advance.