# Binomial Coefficients and 2s

Number Theory Level 5

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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