If you go on the left you will get a draw.

1.Ke2 Kd7
2.Kf3 Ke7
3.Kg4 Kf8
4.Kh5 Kg7
5.Kg5 Kf7
6.Kh6 Ke8
7.Kg7 Ke7
8.Kg6 Kd8
9.Kf7 Kd7
10.Kf6 Kc6
11.Kxe6
It's a win for white. It's very important to go on the right to get the opposition.