For each positive integer
$n$
,
$S(n)$
is the sum of the digits of
$n$
. Positive integer
$a$
is an
**
extra
**
number, if
$\gcd \big(S(a), S(a+1)\big)=k$
, where
$k>1$
. For example 79 is an
**
extra
**
number, because
$\gcd \big(S(79), S(80)\big)=\gcd(16, 8)=8$
.

If
$b$
is the smallest
**
extra
**
number, where
$\gcd(S(b), S(b+1))=10$
, then what is
$S(b)$
?

The answer is 90.

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