k     L   D   L*  D*  LL  DD  DL  LD
0.    1   0   0   0   0   0   0   0
0.    0   1   0   0   0   0   0   0
0.    1   0   1   0   0   0   0   0
0.    0   1   0   1   0   0   0   0
0.    1   0   0   1   0   0   0   0
0.    0   1   1   0   0   0   0   0
0.    0   0   0   0   0   0   1   0
0.    0   0   0   0   0   0   0   1
0.    0   0   0   0   1   0   0   0
0.    0   0   0   0   0   1   0   0