If there are 59 news items, the last merged indexing files should be [tier_5_A, tier_2_A, tier_1_A] "B" file will never appear, because once it appears, it is merged.

tier_1_A=1 file tier_2_A=2 files tier_5_A=16 files

(16+2+1)*3 =57 57+2(still in the memory) = 59