Let $x_{1}, x_{2}, \ldots , x_{2014}$ be positive real numbers such that $\displaystyle \sum_{j = 1}^{2014}x_{j} = 1$. Determine the smallest constant $K$, such that $K \displaystyle\sum_{j = 1} ^ {2014}
\dfrac{ x^2_{j} }{ 1 - x_{j} } \ge 1.$

This problem is taken from RMO 2014.

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