Using generic argument that extends something, stops inferring super keys when Exclude is used in addition to keyof and Pick

TypeScript Version: 3.1.0

Search Terms:
keyof extends pick exclude

Code

interface Base {
    base1: number;
    base2: number;
}

class Data<T extends Base> {
   alpha(k:keyof Pick<T, Exclude<keyof T, "base1">>) {   }
    beta(k:keyof Pick<T, keyof T>) {   }
}

function wrapped<T extends Base>() {
    let d = new Data<T>();
    d.alpha("base2"); // Argument of type '"base2"' is not assignable to parameter of type 'Exclude<keyof T, "base1">'. 
    d.beta("base2");  // works
}

Expected behavior:

Both alpha and beta should work.

Actual behavior:

Alpha does not work: ` Argument of type '"base2"' is not assignable to parameter of type 'Exclude<keyof T, "base1">'.

Playground Link:

Playground link

Related Issues:

Start by reproducing the generic keyof/Pick/Exclude example in the linked TypeScript Playground, using the reported TypeScript version or typescript@next. Trace the type-checking behavior for alpha and beta; the fix is complete when alpha accepts "base2" without an error while beta continues to work.