If \(A\) and \(B\) are two positive integers such that the ratio between the 5-digit integer \(\overline{BBB00} \) and the 3-digit integer \(\overline{AAA} \) is equal to the 3-digit integer \(\overline{B00} \).

Knowign that \(A+A+A=B\), find the value of the product of the two 3-digit integers, \(\overline{ABA}\times \overline{BAB} \).

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