Problem E

Discarding Digits

Stef forms the integer \(N\) by writing the integers from \(1\) to \(50\) in order.

That is,

\(N=1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950.\)

Stef then selects some of the digits in \(N\) and discards them, so that the remaining digits, in their original order, form a new integer. The sum of the digits in this new integer is \(200\).

If \(M\) is the largest integer that Stef could have formed, what are the first ten digits of \(M\)?