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 = s