Binomial Coefficients and 2s

Let \( v_2(n) \) be the highest exponent of \( 2 \) in \( n \). Let

\( \mathfrak{K} = v_2 \left( {2^{2015} \choose 2^{2014}} - {2^{2014} \choose 2^{2013}} \right) \).

Find \( \mathfrak{K} \pmod {1000} \).

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