Pilgrim's Progress

From Numberplay of August 26, 2013.

Pilgrim (red square) must pay 2 coins to go east, but receives two coins when going west. The cost doubles going south, but halves going north. Can the pilgrim exit his pilgrimage from its pilgrimage from NW to SE corner neither owing nor being owed?

Arrow keys to navigate

Cost so far:

Trail ( moves) so far:

Play this (paste comma or space or undelimited sequence of NESW):