Chef and insomnia

Chef sometimes suffers from insomnia. During sleepless nights, he often plays this game: He creates an array A of N integers and also decides one integer K. After that, he tries to count the number of non-empty contiguous subsequences (subsegments) of A, such that there are no bad pairs of integers in this subsegment. A pair (x, y) of integers is called bad if x is situated to the left of y in the