Školjka

%V0 Let $S = \{x_1, x_2, \ldots, x_{k + l}\}$ be a $(k + l)$-element set of real numbers contained in the interval $[0, 1]$; $k$ and $l$ are positive integers. A $k$-element subset $A\subset S$ is called nice if $$\left |\frac {1}{k}\sum_{x_i\in A} x_i - \frac {1}{l}\sum_{x_j\in S\setminus A} x_j\right |\le \frac {k + l}{2kl}$$ Prove that the number of nice subsets is at least $\dfrac{2}{k + l}\dbinom{k + l}{k}$. Proposed by Andrey Badzyan, Russia