Here goes,

$ perl -e'my ($n,$s) = @ARGV; my @foo = map { int($s/$n) + ($_ < $s % 
+$n) }0..$n-1; print "@foo"' 5 13
3 3 3 2 2$
[download]

Purely arithmetic, with a pun on the logical value of '<'.

Or more like the original problem,

@result{@array} = map {
    int($num/@array) + ($_ < $num % @array)
} 0 .. $#array;
[download]