Datasets:

hackercupai
/

hackercup

	Kit is a young, obedient Fox who excels in his studies, diligently practices
	his hunting skills, and is always friendly. His parents couldn't be prouder!
	That is, except for one problem... he refuses to eat his vegetables!

	In an effort to improve Kit's diet, his parents have set up a little game for
	him to play. They've dug a series of 2N \+ 2 small holes in a row on the
	ground, and numbered them from 0 to 2N \+ 1, from first to last. They've
	left the first and last holes empty, and filled the remaining 2N holes
	with one healthy vegetable each! There are N different types of
	vegetables, numbered from 1 to N, and a vegetable of type Vi has
	initially been placed into each hole _i_, such that exactly 2 vegetables of
	each type were used in total.

	Kit must start inside hole 0, and jump forwards from hole to hole until he
	reaches hole 2N \+ 1. When he's inside any given hole _i_, he's agile
	enough to jump to either hole _i_ \+ 1 or directly to hole _i_ \+ 2, but he
	can't jump any further than that at once. Whenever he lands in a hole
	containing a vegetable, the rules of the game mandate that he must eat it!

	Kit has agreed to play this game (not that he has much choice in the matter),
	but there's only so much he can take. The vegetables are tolerable as long as
	there's variety. He doesn't care how many he has to eat in total, but he
	absolutely refuses to eat multiple vegetables of any single type over the
	course of the game. In other words, for each vegetable type, he must only
	enter _at most_ one of the two holes containing that vegetable on his way from
	hole 0 to hole 2N \+ 1.

	Kit will play the game once per day for a period of M days. For some fun
	variety, at the start of each day _i_, his parents will swap the contents of
	two different holes Ai and Bi. Then, Kit will play the game using the
	current configuration of vegetables. Once he's done, his parents will replace
	any vegetables which he had eaten with new vegetables of the same types, thus
	resetting the game to the state it was in before Kit played it.

	Each day, there might be no acceptable way for Kit to complete the game, or
	there might be many different ways for him to do so. Two ways are considered
	different if at least one hole is visited in one but not the other. In order
	to make the game more exciting for himself, Kit would like to count up the
	number of different ways he could potentially complete it each day. However,
	that's a lot of big numbers to keep track of, so he's only interested in the
	sum of these M values when taken modulo 1,000,000,007. Please help him
	compute this overall sum!

	### Input

	Input begins with an integer T, the number of different rows of holes. For
	each row of holes, there is first a line containing the space-separated
	integers N and M. There is next a line containing 2N space-
	separated integers, the _i_th of which is Vi. Then M lines follow, the
	_i_th of which contains the space-separated integers Ai and Bi

	### Output

	For the _i_th row of holes, print a line containing "Case #i: " followed
	by a single integer, the sum of the M days' answers modulo 1,000,000,007.

	### Constraints

	1 ≤ T ≤ 30
	1 ≤ N, M ≤ 500,000
	1 ≤ Ai, Bi ≤ 2N
	1 ≤ Vi ≤ N
	Both the sum of N values and the sum of M values across all T
	cases do not exceed 2,000,000.

	### Explanation of Sample

	In the first case, both holes 1 and 2 will contain vegetables of type 1 even
	after their contents are swapped. There are then 2 different ways for Kit to
	validly reach hole 3 from hole 0, visiting either of these sequences of holes:

	0 -> 1 -> 3
	0 -> 2 -> 3

	He can't quite jump far enough to reach hole 3 directly from hole 0, nor can
	he visit both holes 1 and 2, as that would require eating multiple vegetables
	of a single type.

	In the second case, there are 2 different ways for Kit to validly complete the
	game on the first day, and only 1 way on the second day. This results in a
	final answer of (2 + 1) modulo 1,000,000,007 = 3.