I have a generic function type. I need to convert this type into another, with one more argument prepended to the function:

type FuncType = <T extends any>(arg: T): T;

type FuncWithPrependedArg: ...?

This type should look like this:

type FuncWithPrependedArg = <T extends any>(prepndedArg: any, arg: T): T;

How to derive the second type from the first one dynamically?

I need it because I have an obiect containing different functions and need to create a mapped type for all these functions:

const funcs = {
    funcA: (arg: string): number => {/** ... */},
    funcB: (): string => {/** ... */},
    funcC: <T extends string>(arg: T): T => {/** ... */},
    // ...etc
}

type Funcs: typeof funcs;

type MappedFuncs = SomeTypeToMap<Funcs>;

type SomeTypeToMap = ...?

Is it even possible?