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Algebra Level 4

\[ \large \begin{cases} {A = 1\times 2 + 3\times4 + 5\times 6 + \ldots+37\times38 + 39 } \\ { B = 1 + 2\times 3 + 4 \times 5 + \ldots + 36 \times 37 + 38 \times 39 } \end{cases}\]

The values of \(A\) and \(B\) are obtained by writing multiplcation and addition operators in an alternating pattern between successive integers as described above. Find the absolute difference between \(A\) and \(B\).

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