VMO 1987 Problem 4

$x_1$, $x_2$, ... , $x_n$ are positive reals with sum X and n > 1. h ≤ k are two positive integers. H = $2^h$ and K = $2^k$. Show that $x_1^K$/(X - $x_1$)$^{H-1}$ + $x_2^K$/(X - $x_2$)$^{H-1}$ + $x_3^K$/(X - $x_3$)$^{H-1}$ + ... + $x_n^K$/(X - $x_n$)$^{H-1}$ ≥ $X^{K-H+1}$/( (n-1)$^{2H-1}n^{K-H}$). When does equality hold?