Mr. Chopsticks keeps N monsters, numbered from 1 to N. In order to train them, he holds N * (N - 1) / 2 competitions and asks the monsters to fight with each other. Any two monsters fight in exactly one competition, in which one of them beat the other. If monster A beats monster B, we say A is stronger than B. Note that the “stronger than” relation is not transitive. For example, it is possible that A beats B, B beats C but C beats A.
After finishing all the competitions, Mr. Chopsticks divides all the monsters into two teams T1 and T2, containing M and N – M monsters respectively, where each monster is in exactly one team. Mr. Chopsticks considers a team of monsters powerful if there is a way to arrange them in a queue (A1, A2, …, Am) such that monster Ai is stronger than monster Aj for any 1<=i<j<=m. Now Mr. Chopsticks wants to check whether T1 and T2 are both powerful, and if so, he wants to select k monsters from T2 to join T1 such that the selected monsters together with all the monsters in T1 can still form a powerful team and k is as large as possible. Could you help him?