Given two non-negative integers num1 and num2 represented as strings, return their product as a string — without ever converting the inputs to native integers, since they may be arbitrarily large. The naive approach mirrors long multiplication exactly: multiply num1 by each digit of num2 in turn, shift each partial product into place with trailing zeros, and add everything together with repeated string addition. It works, but every digit triggers a fresh full-length addition. The position arrayPosition ArrayA single array sized to hold every possible digit of the final product, where each pair of input digits is accumulated directly into its known destination positions — no intermediate partial-product strings ever need to be built. technique skips that: since multiplying the digit at position i by the digit at position j always lands at result positions i+j and i+j+1, every digit pair can be accumulated directly into one shared array in a single pass.