Challenge: Digit DP on Multiple Numbers

Count pairs $(a, b)$ where $a \leq X$, $b \leq Y$, and $a + b$ has some property. This is 2D digit DP. Build $a$ and $b$ simultaneously, digit by digit.

State: $(pos, tightA, tightB, carry, ...)$. The carry matters: when checking if $a + b$ has no digit > 5, you need to know if there's a carry from previous positions. Complexity explodes: $O(n \cdot 2 \cdot 2 \cdot 2 \cdot additionalStates)$. Use only when necessary.