Counting Inversions Revisited

Almir had a small sequence $A_1, A_2, \ldots, A_N$. He decided to make $K$ copies of this sequence and concatenate them, forming a sequence $X_1, X_2, \ldots, X_{NK}$; for each valid $i$ and $j$ ($0 \le j \lt K$), $X_{j \cdot N + i} = A_i$. For example, if $A = (1, 2, 3)$ and $K = 4$, the final sequence is $X = (1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3)$. A pair $(i, j)$, where $1 \le i \lt j \le N$,