There are really rush days in the Institute of Parasitic and Symbiotic Creatures (IPSC) this week. They have just discovered new species of bacteria and want to collect as much information about it as possible. Unfortunately the bacteria breed so quickly that one is hardly able to monitor their expansion. So far the institute staff knows only the following few facts about these bacteria:
Your task is to compute how many bacteria will live in each of the colonies after T seconds, provided there is exactly one bacterium in each of them at the beginning.
On the first line there are three integers N, M and T separated by one space. The second line contains one integer K. M lines follow, each of them describes one of the rules according to which the bacteria behave. The description consists of one string and exactly two integers separated by one space. Possible descriptions and their meanings follow.
die i 0All bacteria in the i-th colony die.
reproduce i kThe number of bacteria in the i-th colony increases k times. (1 <= k <= 100)
copy i jIncreases the number of bacteria in the i-th colony by the number of bacteria in the j-th colony.
teleport i jMoves all bacteria from the j-th colony to the i-th colony. (i != j)
swap i jExchanges all bacteria between the i-th and the j-th colony. (i != j)
merry-go-round 0 0Rotates all bacteria to the next colony, i.e. moves all bacteria from the i-th to the i+1-th colony (0 <= i < N-1 ) and moves all bacteria from N-1-st to the 0-th colony. All the moves occur at the same time.
For each colony print one line with the number of bacteria that will live in this colony after T seconds.
8 6 11 7 reproduce 2 5 copy 4 2 die 1 0 merry-go-round 0 0 teleport 5 3 swap 0 2Output file
1 0 0 0 0 4 4 1
The colonies evolved as follows:
|1st||reproduce 2 5||1||1||5||1||1||1||1||1|
|2nd||copy 4 2||1||1||5||1||6||1||1||1|
|3rd||die 1 0||1||0||5||1||6||1||1||1|
|4th||merry-go-round 0 0||1||1||0||5||1||6||1||1|
|5th||teleport 5 3||1||1||0||0||1||4||1||1|
|6th||swap 0 2||0||1||1||0||1||4||1||1|
|7th||reproduce 2 5||0||1||5||0||1||4||1||1|
|8th||copy 4 2||0||1||5||0||6||4||1||1|
|9th||die 1 0||0||0||5||0||6||4||1||1|
|10th||merry-go-round 0 0||1||0||0||5||0||6||4||1|
|11th||teleport 5 3||1||0||0||0||0||4||4||1|