Recursive Digit Sums

Let \(A\) be a number with 2001 digits such that \(A\) is a multiple of \(10!\) Let \(B\) be the digit sum of \(A\), \(C\) be the digit sum of \(B\), and \(D\) be the digit sum of \(C\). What is the unit’s digit of \(D\)?

Details and assumptions

The digit sum of a number is the sum of all its digits. For example the digit sum of 1123 is \(1 + 1 + 2 + 3 = 7\).

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