Infering return type through conditional type of parameter

I'm trying to infer the return type of the function via conditional types. If the type and parameters extend a type, AudioConfig<T> for example - I want the return type to be Audio<T>, otherwise Video<T> and lastly never if type not found.

interface Audio<T extends string> {}
interface Video<T extends string> {}

type AudioConfig<T extends string> = {
    type: 'Audio'
}
type VideoConfig<T extends string> = {
    type: 'Video'
}

type Params<T extends string> =
    | AudioConfig<T>
    | VideoConfig<T>

type Configuration<T extends string, P extends Params<T>> =
    P extends AudioConfig<T> ? Audio<T> :
    P extends VideoConfig<T> ? Video<T> :
    never

type InitConfigurationFn = <T extends string, P extends Params<T>>(params: P) => Configuration<T, P>

const initConfiguration: InitConfigurationFn = (params) => {
    switch (params.type) {
        case 'Audio':
            return { type: 'Audio' }
        case 'Video':
            return { type: 'Video' }
    }
}

Currently initConfiguration function is erroring:

Type '<T extends string, P extends Params>(params: P) => { type: string; }' is not assignable to type 'InitConfigurationFn'. Type '{ type: string; }' is not assignable to type 'Configuration<T, P>'.(2322)

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