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