Set mouse focus and move cursor to end of input using jQuery

This question has been asked in a few different formats but I can't get any of the answers to work in my scenario.

I am using jQuery to implement command history when user hits up/down arrows. When up arrow is hit, I replace the input value with previous command and set focus on the input field, but want the cursor always to be positioned at the end of the input string.

My code, as is:

$(document).keydown(function(e) {
  var key   = e.charCode ? e.charCode : e.keyCode ? e.keyCode : 0;
  var input = self.shell.find('input.current:last');

  switch(key) {
    case 38: // up
      lastQuery = self.queries[self.historyCounter-1];
      self.historyCounter--;
      input.val(lastQuery).focus();
// and it continues on from there

How can I force the cursor to be placed at the end of 'input' after focus?