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sub build_inversion_list_and_index {
  my @invlist;
...
  shift @index;
  return \@invlist, \@index;
}

sub get_nth_char($i, $invlist, $index) {
  return undef if $i >= $index[-1];
...
    else { return $invlist[$mid*2] + ($i - ($mid > 0? $index[$mid-1] :
+ 0)) }
  }
}