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$433x^{2}+y^{2}+\sqrt{1729}xy+\sqrt{3}x-\sqrt{3}y+1729!$

For real values of $x$ and $y$ the above expression attains minimum value at $x=M$ and $y=N$. And $M+N=a\sqrt{b}$, where $a$ is positive integer and $b$ is square-free. Find $a-b$.

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