Difficult path

Alex was very tired after a long day and now, when he reached his street, he realized he had completely lost his sense of direction. Since he cannot remember which way his house is, he chooses a direction randomly. Moreover, at every crossroads, there is a $50\%$ chance that he will keep going forward, or turn around and go back. He is so distracted that he can even walk past his own house without noticing!

After passing $n$ blocks, Alex falls asleep right on the street. When he wakes up, he wonders what were the chances that he slept near his house. From the crossroads where he started his way to the crossroads near his house, there are $m$ blocks. Help him.