Editorial for ICPC NEERC 2010 B - Binary Operation

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Write a procedure to compute for single digits: $\displaystyle a_0 \times \underbrace{a \times a \times \dots \times a}_{c\text{ times}}$
- Repeat multiplies until it loops (after at most $10$ ~10~ muls)
- Use offset and period length to compute the result
Write a procedure to compute for single digits: $\displaystyle a_0 \times \underbrace{a' \times (a+1)' \times \dots \times b'}_{d\text{ times}}$ where $+1$ ~+1~ wraps to $0$ ~0~; and $a'$ ~a'~ means " $a \times a \times \dots \times a$ ~a \times a \times \dots \times a~" $c$ ~c~ times (as above)
- Compute loop similarly (can be as long as $100$ ~100~)
Compute the result digit by digit using two of the above procedures
- For a digit $i$ ~i~, round the number $a$ ~a~ up and $b$ ~b~ down to the nearest multiple of $10^i$ ~10^i~
- Represent the number range $[a, b]$ ~[a, b]~ as:
  - $X \dots XXaXX \dots X$ ~X \dots XXaXX \dots X~
  - $X \dots XX(a+1)00 \dots 0$ ~X \dots XX(a+1)00 \dots 0~
  - $X \dots XXb00 \dots 0$ ~X \dots XXb00 \dots 0~
  - $X \dots XXbXX \dots X$ ~X \dots XXbXX \dots X~

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