Number literal type sum bug

TypeScript Version: 4.12

Search Terms:
Sum, literal, not working correct

Code

namespace Shared {
  export type Num = string | number | bigint;

  export type Preformat<T extends Shared.Num, U extends string = `${T}`, Acc extends string[] = []> = U extends `${infer Head}${infer Rest}`
    ? Preformat<T, Rest, [Head, ...Acc]>
    : Acc

  export type Helper<T, U0, U1, U2, U3, U4, U5, U6, U7, U8, U9> = 
    T extends '0' ? U0 : T extends '1' ? U1 : T extends '2'
                  ? U2 : T extends '3' ? U3 : T extends '4'
                  ? U4 : T extends '5' ? U5 : T extends '6'
                  ? U6 : T extends '7' ? U7 : T extends '8'
                  ? U8 : T extends '9' ? U9 : never

  export type HelperMap<R> = R extends [infer T, infer U]
    ? Shared.Helper<
        T,
        Shared.Helper<U, ['0', false], ['1', false], ['2', false], ['3', false], ['4', false], ['5', false], ['6', false], ['7', false], ['8', false], ['9', false]>,
        Shared.Helper<U, ['1', false], ['2', false], ['3', false], ['4', false], ['5', false], ['6', false], ['7', false], ['8', false], ['9', false], ['0', true]>,
        Shared.Helper<U, ['2', false], ['3', false], ['4', false], ['5', false], ['6', false], ['7', false], ['8', false], ['9', false], ['0', true], ['1', true]>,
        Shared.Helper<U, ['3', false], ['4', false], ['5', false], ['6', false], ['7', false], ['8', false], ['9', false], ['0', true], ['1', true], ['2', true]>,
        Shared.Helper<U, ['4', false], ['5', false], ['6', false], ['7', false], ['8', false], ['9', false], ['0', true], ['1', true], ['2', true], ['3', true]>,
        Shared.Helper<U, ['5', false], ['6', false], ['7', false], ['8', false], ['9', false], ['0', true], ['1', true], ['2', true], ['3', true], ['4', true]>,
        Shared.Helper<U, ['6', false], ['7', false], ['8', false], ['9', false], ['0', true], ['1', true], ['2', true], ['3', true], ['4', true], ['5', true]>,
        Shared.Helper<U, ['7', false], ['8', false], ['9', false], ['0', true], ['1', true], ['2', true], ['3', true], ['4', true], ['5', true], ['6', true]>,
        Shared.Helper<U, ['8', false], ['9', false], ['0', true], ['1', true], ['2', true], ['3', true], ['4', true], ['5', true], ['6', true], ['7', true]>,
        Shared.Helper<U, ['9', false], ['0', true], ['1', true], ['2', true], ['3', true], ['4', true], ['5', true], ['6', true], ['7', true], ['8', true]>
      >
    : never

  export type Join<T, Acc extends string = ''> = T extends [infer Head, ...infer Rest]
    ? Head extends string 
      ? Join<Rest, `${Acc}${Head}`>
      : never
    : Acc

  export type JoinR<T, Acc extends string = ''> = T extends [infer Head, ...infer Rest]
    ? Head extends string 
      ? JoinR<Rest, `${Head}${Acc}`>
      : never
    : Acc
}

namespace Sum {
  type Nulling<T> = {
    [K in keyof T]: "0"
  }

  type Concat<T extends any[], U extends any[]> = [...T, ...U]

  type Liner<T extends any[], U extends any[]> = Concat<T, Nulling<U>>

  type Zip<T, U> = {
    [K in keyof T]: K extends keyof U
      ? [T[K], U[K]]
      : never
  }

  type Iter<T, B extends boolean = false, Acc extends any[] = []> = T extends [infer Head, ...infer Rest]
    ? B extends true
      ? Iter<Rest, Shared.HelperMap<[Shared.HelperMap<Head>[0], "1"]>[1], [...Acc, Shared.HelperMap<[Shared.HelperMap<Head>[0], "1"]>[0]]>
      : Iter<Rest, Shared.HelperMap<Head>[1], [ ...Acc, Shared.HelperMap<Head>[0]]>
    : Acc

  type Unformate<T, Acc extends any[] = []> = T extends [infer Head, ...infer Rest]
    ? Unformate<Rest, [Head, ...Acc]>
    : Acc

  type Cut<T> = T extends [infer Head, ...infer Rest]
    ? Head extends '0'
      ? Cut<Rest>
      : T
    : ['0']

  export type Sum<
      A extends Shared.Num, 
      B extends Shared.Num,
      PA extends string[] = Shared.Preformat<A>,
      PB extends string[] = Shared.Preformat<B>,
      LA = Liner<PA, PB>,
      LB = Liner<PB, PA>,
      Z = Zip<LA, LB>,
      I = Iter<Z>,
      U = Unformate<I>,
      C = Cut<U>,
      J = Shared.Join<C>
    > = J
  
  type testSum = [
    Sum<"90", "9">,
    Sum<"0", Sum<"9", Sum<"90", Sum<"900", "9000">>>>
  ]
}

namespace Multiply {
  type Piper<T, Acc extends string = '0', Debug extends any[] = []> = T extends [infer Head, ...infer Rest]
    ? Head extends string
      ? Piper<Rest, Sum.Sum<Head, Acc>, [...Debug, [Head, Acc, Rest, Sum.Sum<Head, Acc>]]>
      : never
    : Acc

  type testPiper1 = [
    Piper<["9", "90"]>,
  ]
}

Expected behavior:

Looks first on two main types: Sum.Sum and Piper. When i use Piper with ["9", "90"] its return strange result like "999", but must "99". I tested my Sum.Sum type and it work correct

Then look on Piper Debug type. Looks like on first iteration they have correct Head and Rest types, but result incorrect

  type Piper<T, Acc extends string = '0', Debug extends any[] = []> = T extends [infer Head, ...infer Rest]
    ? Head extends string
      ? Piper<Rest, Sum.Sum<Head, Acc>, [...Debug, [Head, Acc, Rest, Sum.Sum<Head, Acc>]]>
      : never
+    : Debug

Actual behavior:
Piper<["9", "90", "900", "9000"]> must return correct value "9999" like Sum<"0", Sum<"9", Sum<"90", Sum<"900", "9000">>>>

Playground Link: https://www.typescriptlang.org/play?#code/HYQwtgpgzgDiDGEAEBlAFiAThAJkg3gLABQSSEAHjAPaYAuSdAnjMgHICuYSAvElHUwBLYAHMkAHyTAuAIwiZJSWUNEi6AbhIkylGvUYtkABWwAzWmBB0APABVyFOhGA4oqDNhwA6TmAA0SACqjs6u7gLCYrxIAAYAJPh2AL6xgQCC8PChLm78giKiANoAujGlAHwxIZRheQn4ImYKSAASECA4yYlNLQBK0HSpOmRIAPxIphAWmFa2doEDAoFF7Z2B3puZ8CUVI2QAXEjb2qSO+gzMrG0QADasmPaBQQAMzwCMzwBMzwDMzwAWZ4AVmeADZngB2Z4ADmeAE4qnx9kgHLVcu4AOQvTHjYIvJBHNFODFITHvXETILvQmonLhMlfTEo0astlkKlfWnEupY36U4K-bn0vKYgHMs7sqWjKkA4XohmY4ECoLA+UkxVgiXSnV4oJg9W8smQlWQw2kzEw7W6qVUmHmxXwlXw2nACAANwUp10VFolyMN3uCgAsiAYDY+kikH0Re4ir1FAskAngiUURN0FhcN52kHHizRgsC2RM14c3cHjYgitsZjAmYQLcoBASjWKfXG83W0gipimR2my2a-yB12a+LR0Oe0q60gG4Pu72tZPF5iTSua1aN9OnSuKv5ix4sz5c5Xq9P23PO1Pe-2rwvh7P52PpxP7y-e8rt0un9fV+v3xvS1fwfHcQI-WtAkEDgW33Q9S2zU8FCrGs72fICR0A1c33Q1cvywmtlwI6cANwzdwKA3diN7HEoMwGDV0vaDYIPSU2QQk8K2Q89e0wsjXwovDBMI4SSNE3st2ozEqP4mjZ2Yxj5PooC7wUuC2NZDjyzzFCBO-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-PrgAGREZDZbySvq+7GoNT7+vdhiIuS7LpNA+DsQqwqL72+QAAtIRwyTIIw5RKOY-jxPk9To5o919wE6TlOgkNoo7Cjwfb4123pA5-6zlzpekAASWcR4kwAIRh2Q1BqC3A6LHPg6EMjQxPkgfupRyhjz4L3OMKYsY41Vujfo6t0xIH-tA5ihsv7IVNjNPMoZwxFBIQ8MhNgsYVCKC8bs6d3jp12EUd4i4VbbECJQkMYYbAUIaidXh4ZaH0MYcw1hDDdgFiOIQx4xDBFeWoaI9hKxlZbCyNwxRGVlHazoVIm2hxuYA39kEdGlhrAQFFlA4e7hYFlD4A3RBMN5YtFQeo9BCt8YPw5MEcxsxLERkGCsdxnCsjSK5k7d+BcODzGRi4lB2s0FqwED4vEJNoG1kNjE2w+NDGjCJA7acOI25nD5gYf23swA2ALOkGGWk-CBALLg2xR4yyNILMYOp0D9bFAcW07MUwZhzBsOkFKbJjAtKNL0uBfAtJDIsbYX+4zWQdzqXwLubpHhdMCJMlZowO7-w2d3bZv9dljPcmyZeMRV7hjWYEQ5+yyAfxiHImwy8nnBGqP4uYViP6fILuPWJ89LmshBjELSQsbAF3yVGEGIx37OAEFU8oKIqk2HTvCLOgRMXp32eizO6duFcAxfCIlqASWYuxRS6pVLqV0qzgvBeIxCZv2IG7aAcBEBIGDBwW4dA163CYL7M4-tjBrx7pA7IPSJbwzJNZAAIhAWQHBxDQPsfA+J0DXGYySR4lJBNsEZNab0w24rKzEK4N4dF7jtj7h7CrJVKrRAhL1Vw6MwSaXWpJQ0ZmaQzb4CthUEoES2ZP3tlzJ1qqTEBiRXQc1CgaSOJRAmx4RRcU4qxSw8ZrKgA

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