Sereja and Inversions

Sereja has a permutation P of the N numbers in the range 1 to N. You have to answer M queries over it, where each query is given four numbers l1, r1, l2, r2 (1 ≤ l1 ≤ r1 2 ≤ r2 ≤ N, r1 - l1 = r2 - l2). Your task is to calculate number of permutations Q of the S integers in the range 1 to S, such that S = r1 - l1 + 1, and for each i from 1 to S, the condition PQi + l1 - 1 i + l2 - 1 is satisfied.