There are several test cases. In the first line of each case there are two integers K (1 <= K <= 20) and N (2 <= N <= 10). Then follows a line with K integers expressing the password. Each number in the password is between 1 and N. Then come K lines, the i-th of which describes how the i-th dial plate controls the referred gears. These K lines have the following format:

p a1 b1 a2 b2 ... ap bp

Integer p (0 <= p <= K) expresses the number of gears that are referred to the dial plate. ai (1 <= i <= p) is an integer between 1 and K which tells that the ai-th gear is under the control of this dial plate. bi is an integer between 1 and N-1 which tells that when the dial plate is dialed once, the ai-th gear will rotate across by bi gears.

A test case of K = 0 and N = 0 indicates the end of input, and should not be processed.

p a1 b1 a2 b2 ... ap bp

Integer p (0 <= p <= K) expresses the number of gears that are referred to the dial plate. ai (1 <= i <= p) is an integer between 1 and K which tells that the ai-th gear is under the control of this dial plate. bi is an integer between 1 and N-1 which tells that when the dial plate is dialed once, the ai-th gear will rotate across by bi gears.

A test case of K = 0 and N = 0 indicates the end of input, and should not be processed.