To complete the utility type `P` in TypeScript, we can use a mapped type:

```typescript
interface A {
  k1: 0;
  k2: 1;
}

type P<T, V> = {
  [K in keyof T]: V;
};

const a: P<A, string> = {
  k1: 'dogs',
  k2: 'cats',
};
```

In this example, the `P<T, V>` utility type takes two type parameters `T` and `V`. It uses a mapped type to iterate over each key `K` of `T` and assigns the value type `V` to each key.

However, there is an error in the code you provided since you are trying to assign string values to keys that have values of type `0` and `1` in interface `A`. If you want to enforce the values of `k1` and `k2` to be `'dogs'` and `'cats'` respectively, you can modify the code as follows:

```typescript
interface A {
  k1: 'dogs';
  k2: 'cats';
}

type P<T, V> = {
  [K in keyof T]: V;
};

const a: P<A, string> = {
  k1: 'dogs',
  k2: 'cats',
};
```

Now, the `P` type ensures that the values assigned to `k1` and `k2` must match the specified string values.