B'The map of Europe can be represented by a set of n cities, numbered from 1 through n , which are connected by m bidirectional roads, each of which connects two distinct cities. A trip of length k is a sequence of k+1 cities v_1, v_2, ldots, v_{k+1} such that there is a road connecting each consecutive pair v_i , v_{i+1} of cities, for all 1 <= i <= k . A special trip is a trip that does not use the same road twice in a row, i.e., a sequence of k+1 cities v_1, v_2, ldots, v_{k+1} such that it forms a trip and v_i neq v_{i + 2} , for all 1 <= i <= k - 1 . Given an integer k , compute the number of distinct special trips of length k which begin and end in the same city. Since the answer might be large, give the answer modulo 998 ,244 ,353 . The first line contains three integers n , m and k ( 3 <= n <= 100 , 1 <= m <= n(n - 1) / 2 , 1 <= k <= 10^4 ) -- the number of cities, the number of roads and the length of trips to consider. Each of the following m lines contains a pair of distinct integers a and b ( 1 <= a, b <= n ) -- each pair represents a road connecting cities a and b . It is guaranteed that the roads are distinct (i.e., each pair of cities is connected by at most one road). Print the number of special trips of length k which begin and end in the same city, modulo 998 ,244 ,353 . In the first sample, we are looking for special trips of length 2 , but since we cannot use the same road twice once we step away from a city we cannot go back, so the answer is 0 . In the second sample, we have the following 12 special trips of length 3 which begin and end in the same city: (1, 2, 4, 1) , (1, 3, 4, 1) , (1, 4, 2, 1) , (1, 4, 3, 1) , (2, 1, 4, 2) , (2, 4, 1, 2) , (3, 1, 4, 3) , (3, 4, 1, 3) , (4, 1, 3, 4) , '...