func add_with_carry(result, addend, addendpos) {
    loop {
        while (result.len < addendpos+1) {
            result.append(0)
        }
        var addend_digits = (addend.to_i + result[addendpos] -> to_s.chars)
        result[addendpos] = addend_digits.pop
        addend_digits.len > 0 || break
        addend = addend_digits.pop
        addendpos++
    }
}
 
func longhand_multiplication(multiplicand, multiplier) {
 
    var result = []
    var multiplicand_offset = 0
 
    multiplicand.reverse.each { |multiplicand_digit|
        var multiplier_offset = multiplicand_offset
        multiplier.reverse.each { |multiplier_digit|
            var multiplication_result = (multiplicand_digit.to_i * multiplier_digit.to_i -> to_s)
 
            var addend_offset = multiplier_offset
            multiplication_result.reverse.each { |result_digit_addend|
                add_with_carry(result, result_digit_addend, addend_offset)
                addend_offset++
            }
            multiplier_offset++
        }
        multiplicand_offset++
    }
 
    return result.join.reverse
}
 
say longhand_multiplication('18446744073709551616', '18446744073709551616')