
ZOJ Problem Set  2699
Once upon the time there lived a king and he had a big kingdom. And there were n cities in his kingdom and some of them were connected by the roads. And the roads were all oneway because it would be dangerous if two carriages riding in opposite directions met on a road. And once the king decided that he would like to establish police in his country and ordered to build police stations in some cities. But since his finances are limited, he would only like build police stations in k different cities. He would like to build them in such a way, that the following conditions were satisfied:
Now the king wants to know how many different ways are there to do so. Help him to find the answer to this question. Input There are mutilple cases in the input file. The first line of each case contains n , m and k  the number of cities and roads in the kingdom, and the number of police stations to build, respectively (1 <= n <= 100 , 0 <= m <= 20,000 , 1 <= k <= n ). The following m lines contain two city numbers each and describe roads, remember that it is only possible to travel along roads in one direction  from the first city to the second one. Two cities may be connected by more than one road. There is an empty line after each case. Output Output the only integer number  the number of ways to fulfil king's request. There should be an empty line after each case. Sample Input 6 7 3 1 2 2 3 3 1 3 4 4 5 5 6 6 5 Sample Output 15 Source: Andrew Stankevich's Contest #9 