Everybody knows how to play tic-tac-toe. If accidentally you do not know the rules of this game, you can always consult Wikipedia. In this problem we will use a slightly different version of tic-tac-toe. First, the game board is not limited to 3 × 3 cells, but considered infinite. Also in order to win a player must get not 3 but at least k noughts or crosses in a line (horizontal, vertical or diagonal). In modified tic-tac-to version it is not so easy to determine a winner. So in this problem you will be given a list of turns performed by the players during the game and you need to determine the winner. Input There is a number of tests T (T ≤ 100) on the first line. Each test case is described by the two numbers n k (n ≤ 105, k ≤ 5), where n stands for number of turns for both players and k for winning line size. Next line contains n pairs of signed 32-bit integers x y — coordinates of each players turn. All turns have been performed sequentially by both players and crosses have always started a game. Output For each test case output a single line ‘Case T: S’. Where T is the test case number (starting from 1) and S is equal to ‘crosses’ or ‘noughts’ if one of them has a winning line. If nobody yet has won a game output ‘none’ and if both players have winning lines output ‘error’ for S. Sample Input 2 32 001110 42 0 0 -1 0 1 1 -1 1 Sample Output Case 1: crosses Case 2: error