Trouble is caused by initialisation, so what data structure to use that is initialized in constant time? The answer may be to use simple strings for A and B. The length should be U*log_10(U) so that each group of log_10(U) characters represents an "array element". Initialisation can be done using pack that should be constant time, array access can be simulated using substr which is also constant time.
Just my 2 cents, might be totally wrong, -gjb-
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