High-ability and low-ability

Suppose there are two types of workers: high-ability and low-ability. Workers know their own abilities but firms do not. A high school diploma costs a high-ability person $10,000 and costs a low-ability person $15,000. Firms wish to use education as a screening device where they intend to pay $20,000 a year to high school drop-outs and $K to those with a high school diploma.

1. What value of $K guarantees that low-ability workers don’t have an incentive to finish high school, thus revealing their true type?
2. What value of $K guarantees that high-ability workers have an incentive to finish high school, thus revealing their true type?
3. In what range must K be to make this an effective way of telling apart the two types of workers (separating equilibrium)?