Problem Statement

You are given a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1, \\dots, N$, and the $i$-th $(1 \\leq i \\leq M)$ edge connects Vertices $U_i$ and $V_i$.

There are $2^N$ ways to paint each vertex red or blue. Find the number, modulo $998244353$, of such ways that satisfy all of the following conditions:

• There are exactly $K$ vertices painted red.
• There is an even number of edges connecting vertices painted in different colors.

Constraints

• $2 \\leq N \\leq 2 \\times 10^5$
• $1 \\leq M \\leq 2 \\times 10^5$
• $0 \\leq K \\leq N$
• $1 \\leq U_i \\lt V_i \\leq N \\, (1 \\leq i \\leq M)$
• $(U_i, V_i) \\neq (U_j, V_j) \\, (i \\neq j)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $K$ $U_1$ $V_1$ $\\vdots$ $U_M$ $V_M$

Output

Print the answer.

Sample Input 1

4 4 2
1 2
1 3
2 3
3 4

Sample Output 1

2

The following two ways satisfy the conditions.

• Paint Vertices $1$ and $2$ red and Vertices $3$ and $4$ blue.
• Paint Vertices $3$ and $4$ red and Vertices $1$ and $2$ blue.

In either of the ways above, the $2$-nd and $3$-rd edges connect vertices painted in different colors.

Sample Input 2

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

Sample Output 2

64