Gretchen, a little peasant girl from the Swiss Alps, is an expert at the Daisy game, a simple game that is very well-known around the country. Two players pluck of the petals of a Daisy fower, and each player is always at liberty to pluck a single petal or any two contiguous ones, so that the game would continue by singles or doubles until the victorious one takes the last leaf and leaves the “stump”—called the “old maid”— to the opponent. The pretty mädchen has mastered the Daisy game to such an extent that she always plays optimally. In other words, she always plays by performing the best possible moves on each turn, a feat which never fails to astonish tourists who dare to challenge her to a game. Little Gretchen playing the Daisy game Analyzing the game, it is not very complicated to fgure out a winning strategy for the second player, as long as the game starts with a complete fower (having all of its petals intact). However, what will happen when Gretchen plays against an opponent that also plays optimally, and some of the fower’s petals have been plucked of at random? A fower is described by a number N which represents the original number of petals of the fower, and a list of the petals that have been plucked of. All petals are numbered from 1 to N, and given the circular nature of the fower, that means petals 1 and N are originally adjacent. Given the description of a fower, and assuming it’s Gretchen’s turn, will she win the game? Re- member that both players always play optimally. Input Input starts with a positive integer T, that denotes the number of test cases. Each test case begins with two integers in a single line, N and M, representing the number of petals originally in the fower, and the number of petals that have been plucked of, respectively. The next line contains M distinct integers, representing the petals that have been plucked of. These numbers will always be in ascending order. T ≤ 5000; 3 ≤ N ≤ 20; 1 ≤ M < N Output For each test case, print the case number, followed by the string ‘yes’ if Gretchen wins the game, or ‘no’ otherwise. Sample Input 2 13 1 7 53 134
2/2 Sample Output Case 1: yes Case 2: no