Beats and Pieces

Chef has an array of $N$ integers $[A_1, A_2, \dots, A_N]$. He wants to perform $M$ operations; for each $i$ ($1 \le i \le M$), the $i$-th operation consists of reversing the subarray $[A_{l_i}, \dots, A_{r_i}]$. Each operation should be applied exactly once. However, Chef does not remember the order in which they should be applied, so he wants to choose a uniformly random permutation of the $M$