Here is simple synthetic function

function test(input) {
    if (typeof input === 'number') {
        return 'a'
    } else {
        return input
    }
}

I want to type it but cannot figure out approach. The best I was able to get is:

function test<T extends Number>(input: T): string;
function test<T>(input: T): T;
function test(input) {
    if (typeof input === 'number') {
        return 'a'
    } else {
        return input
    }
}

const a = [test('2'), test(2), test(null), test(true)] as const
//    ^? a: readonly ['2', string, null, true]
// looks valid

const b = [test<string>('2'), test<boolean>(true)] as const
//    ^? b: readonly [string, boolean]
// I can control/generalize types!

The blot on the landscape for that solution looks like that:

Parameter ‘input’ implicitly has an ‘any’ type.

What am I missing here? How to make Typescript happy while keeping types consistent and reliable?