IMO 1967 - Longlist Problems Question 30

(MON 1) Given $m+n$ numbers $a_i$ ($i=1,2,\ldots,m$), $b_j$ ($j=1,2,\ldots,n$), determine the number of pairs $(a_i,b_j)$ for which $|i-j|\ge k$, where $k$ is a nonnegative integer.