1014 - KPath

Time Limit: 1s Memory Limit: 512MB

Submissions: 419 Solved: 116
Description

A k-path on a given undirected graph is a path having exactly k edges and containing no repeated nodes. Given an undirected graph G and an integral value k, count how many k-paths on G.

 

Input

The input consists of following lines:

Line 1: contains two integer n and k (1 ≤ n≤ 30, 1 ≤ k ≤ 10) in which n is the number of nodes of the graph G (nodes are numbered 1,2,...,n);

Line 2: contains an integer m (1 ≤ m ≤ 60) which is the number of edges of G;

Line i+2: contains two integers u and v representing two end points of the ith edge of G (i = 1,2,...,m).

Output

The output contains the number of k-paths of G.

Sample Input
4 3
5
1 2
1 3
1 4
2 3
3 4
Sample Output
6
Hint
Source