시간 제한메모리 제한제출정답맞힌 사람정답 비율
5 초 512 MB116654.545%

## 문제

Um_nik has a simple connected undirected graph with the following property:

For any subset A of k + 1 vertices of the graph, there exist two vertices a, b ∈ A and some edge e, such that all paths from a to b contain edge e.

## 입력

The first line contains three integers n, m, k: the number of vertices and edges in the graph and the given parameter (1 ≤ n ≤ 25 000, n − 1 ≤ m ≤ 500 000, 1 ≤ k ≤ 25).

The next m lines describe edges of the graph. Each of them contains two integers u and v: the two vertices connected by an edge (1 ≤ u, v ≤ n, u ≠ v).

It is guaranteed that this graph is connected and also for any subset A of k+ 1 vertices of the graph, there exist two vertices a, b ∈ A and an edge e such that all paths from a to b contain edge e. It is guaranteed that this graph doesn’t contain multiple edges.

## 출력

Print a single integer: the determinant of Um_nik graph’s adjacency matrix modulo 998 244 353.

## 예제 입력 1

4 3 1
1 2
2 3
3 4


## 예제 출력 1

1


## 예제 입력 2

6 6 3
2 3
5 6
2 5
1 2
3 4
6 2


## 예제 출력 2

998244352


## 예제 입력 3

10 15 10
1 8
1 7
6 7
2 8
6 9
1 2
4 9
4 10
4 6
5 6
3 8
9 10
8 10
3 5
2 7


## 예제 출력 3

35


## 출처

• 문제를 만든 사람: 300iq