level=0 a=1
level=1 a=0.5,0.5
level=2 a=0.75,0.25
level=3 a=0.33333,0.33333,0.33333
level=4 a=0.5,0.25,0.25
level=5 a=0.875,0.125
level=5 a=0.625,0.375