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문제

Alice and Bob live in a city with N intersections (numbered as intersection 1, intersection 2,..., intersection N). There are M roads. Each road is bidirectional and directly joins two intersections. Each pair of intersections is joined by at most one road.

Alice lives in a house at intersection 1. Bob lives in a house at intersection N. They start wandering in the city at 12pm. Each minute each one move from one intersection to another which is connected directly by a road. (Note that since they have to move, they cannot stay at the same intersection they were at in the previous minute).

They agree to meet exactly T minutes after 12pm at some intersection. Also they do not want to meet each other before T minutes. In how many ways can they move inside the city? Note that because they travel fairly fast, they do not meet if they travel on the same road on different directions.

입력

The first line of the input contains an integer K (1<=K<=5), the number of test cases. Then K test cases
follow in the format specified below.

Each test case starts with 3 integers N, M, and T (2<=N<=10; 1<=M<=50; 1<=T<=1,000,000,000,000). The next M lines specify road connections. That is, line 1+i, for 1<=i<=M, contain two integers A and B specifying that there is a bidirectional road connecting intersection A and B (1<=A<=N; 1<=B<=N; A is not equal to B).

출력

For each test case, your program should output the number of possible ways (modulo 9973) can Alice and Bob move in the city so that at time T they meet at some intersection but they do not meet at any intersection before that. Since the number can be very large, you should output the numbers modulo 9973.

 

예제 입력

4
3 3 2
1 2
2 3
1 3
3 2 2
1 2
2 3
4 4 10
1 2
2 4
1 3
4 3
4 5 1000
1 2
2 4
1 3
4 3
1 4

예제 출력

3
0
1024
3213

힌트