type GetFirst<A extends string[]> = A extends [infer Head, ...infer _] 
    ? Head extends string
        ? Head
        : null
    : null;
type GetLast<A extends string[]> = A extends [...infer _, infer Last] 
    ? Last extends string
        ? Last
        : null
    : null

type PopLast<A  extends string[]> = A extends [...infer Rest, infer _] 
    ? Rest extends string[] 
        ? Rest
        : []
    : []

/**
 * type sumOf1Add9 = AddTable[1][9] // 10
 */
type AddTable = [
  [0,  1,  2,  3,  4,  5,  6,  7,  8,  9],
  [1,  2,  3,  4,  5,  6,  7,  8,  9, 10],
  [2,  3,  4,  5,  6,  7,  8,  9, 10, 11],
  [3,  4,  5,  6,  7,  8,  9, 10, 11, 12],
  [4,  5,  6,  7,  8,  9, 10, 11, 12, 13],
  [5,  6,  7,  8,  9, 10, 11, 12, 13, 14],
  [6,  7,  8,  9, 10, 11, 12, 13, 14, 15],
  [7,  8,  9, 10, 11, 12, 13, 14, 15, 16],
  [8,  9, 10, 11, 12, 13, 14, 15, 16, 17],
  [9, 10, 11, 12, 13, 14, 15, 16, 17, 18],
]

type StringOneDigitMap = {'0': 0, '1': 1, '2': 2, '3': 3, '4': 4, '5': 5, '6': 6, '7': 7, '8': 8, '9': 9}
type StringOneDigit = keyof StringOneDigitMap
type StringOneDigitToNum<A extends string | null> = A extends StringOneDigit ? StringOneDigitMap[A]: 0;

type ToString<A extends number | string | bigint> = `${A}`

/**
 * type splitStr = SplitString<'2034'> // ['2', '0', '3', '4']
 */
type SplitString<A extends string, Result extends string[] = []> = 
    A extends `${infer Head}${infer Tail}` 
        ? SplitString<Tail, [...Result, Head]>
        : Result

type AddStringOneDigits<A extends string | null, B extends string | null> = 
    A extends null
        ? B extends null
            ? null
            : B
    :ToString<AddTable[StringOneDigitToNum<A>][StringOneDigitToNum<B>]>;

type addStringOneDigits = AddStringOneDigits<'1', '9'>

type Carry<A extends string | null, Split = A extends string ? SplitString<A>: null> = 
    Split extends StringOneDigit[]
        ? Split['length'] extends 2
            ? `${Split[0]}${AddStringOneDigits<Split[1], '1'>}`
            : `${AddStringOneDigits<Split[0], '1'>}`
        : A

type _Add<
    A extends string[],
    B extends string[],
    Result extends string = '',
    Carrying extends boolean = false,
    res2 extends any[] = [],
    _Sum extends string | null = AddStringOneDigits<GetLast<A>, GetLast<B>>,
    Sum extends string | null = Carrying extends true ? Carry<_Sum> : _Sum,
    SplitSum extends StringOneDigit[] | null = Sum extends string ? SplitString<Sum>: null
> =
    SplitSum extends StringOneDigit[]
        ? _Add<PopLast<A>, PopLast<B>, `${GetLast<SplitSum>}${Result}`, SplitSum['length'] extends 2 ? true : false, [...res2, {A:A,B:B,Result:Result,Carrying:Carrying}]>
        : Carrying extends true
            ? `1${Result}` 
            : Result

type Sum<A extends number | string | bigint, B extends number | string | bigint> = _Add<SplitString<ToString<A>>, SplitString<ToString<B>>>

import type { Equal, Expect } from '@type-challenges/utils'

type cases = [
  Expect<Equal<Sum<2, 3>, '5'>>,
  Expect<Equal<Sum<'13', '21'>, '34'>>,
  Expect<Equal<Sum<'328', 7>, '335'>>,
  Expect<Equal<Sum<1_000_000_000_000n, '123'>, '1000000000123'>>,
  Expect<Equal<Sum<9999, 1>, '10000'>>,
  Expect<Equal<Sum<4325234, '39532'>, '4364766'>>,
  Expect<Equal<Sum<728, 0>, '728'>>,
  Expect<Equal<Sum<'0', 213>, '213'>>,
  Expect<Equal<Sum<0, '0'>, '0'>>,
]