How to key ReadonlyArray type by 'id' key?

KeyBy.ts

/*
 *
 * I want to key array by 'id'
 * 
 * FROM: [{id: 'a', name: 'A'}, {id: 'b', name: 'B'}]
 * TO: { a: {id: 'a', name: 'A'}, b: {id: 'b', name: 'B'} }
 * 
 */

const arr = [{id: 'a', name: 'A'}, {id: 'b', name: 'B'}] as const
type Arr = typeof arr;
type K = Extract<keyof Arr, number>;

type KeyBy<Arr extends ReadonlyArray<{id: string, name: string}>> = {
    [K in Arr[number]['id']]: Extract<Arr[number], {id: K}>
}

type Res = KeyBy<Arr> 

const a: Res = {
    a: {id: 'a', name: 'A'},
    b: {id: 'b', name: 'B'}
}