Good luck guessing
Let \(N\) be the smallest positive integer that is divisible by \(128\) and has digit sum equal to \(128.\) In decimal notation, \( N \) consists of \(a\) \(8\)'s, \(b\) \(9\)'s and possibly some other digits. What is \( a \times b\)?
Details and assumptions
In decimal notation, \( 128289\) consists of \(2\) \(8\)'s, \(1\) \(9\)'s and some other digits.