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Magic Bracelet
Description Ginny¡¯s
birthday is coming soon. Harry Potter is preparing a birthday present
for his new girlfriend. The present is a magic bracelet which consists
of n magic beads. The are m kinds of different magic
beads. Each kind of beads has its unique characteristic. Stringing many
beads together a beautiful circular magic bracelet will be made. As
Harry Potter¡¯s friend Hermione has pointed out, beads of certain
pairs of kinds will interact with each other and explode, Harry Potter
must be very careful to make sure that beads of these pairs are not
stringed next to each other. There infinite beads of each kind.
How many different bracelets can Harry make if repetitions produced by
rotation around the center of the bracelet are neglected? Find the
answer taken modulo 9973. Input The first line of the input contains the number of test cases. Each test cases starts with a line containing three integers n (1 ¡Ü n ¡Ü 109, gcd(n, 9973) = 1), m (1 ¡Ü m ¡Ü 10), k (1 ¡Ü k ¡Ü m(m − 1) ⁄ 2). The next k lines each contain two integers a and b (1 ¡Ü a, b ¡Ü m), indicating beads of kind a cannot be stringed to beads of kind b. Output Output the answer of each test case on a separate line. Sample Input Sample Output Source |
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