×_7_12_2013 A:UFO's Profit

Problem A: UFO's Profit

Time Limit: 1 Sec   Memory Limit: 128 MB
Submit: 13   Solved: 3
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Description

UFO likes traveling by bike very much. He intends to travel this summer. Due to lack of money, he must 

bring things and exchange them with others. When he arrives in a city, he sells everything he has and buys 

new things. Then he travels to another city, sells his items and buys new ones.  

In this problem you will have to find the total amount of money UFO will gain on the optimal tour. On a 

tour he can go to some city more than once, and he must finish his tour in some cities. Also there is a starting 

city for his tour and the number of inter-city travels he wants to do in his tour. 

Input

The input file contains several test cases. The first line is N: the number of test cases. Then follows N cases. 

The description of each case is given below:  

Each case starts with four integers C (2 <= C <= 100), the number of cities, and the cities are numbered 

from 1 to C, S (1 <= S <= C), the identifier of the starting city, E (1 <= E <= C-1), the number of cities his 

tour can end at, and T (1 <= T <= 1000), the number of inter-city travels he wants to do.  

Follow C lines with C non-negative integers which are no more than 1000. The jth integer of the ith line will 

describe the profit he earns when he goes from city i to city j by selling things. As he does not want to make 

a trip to a city he is already, the ith integer of the ith line will always be 0. Note that going from city i to city j 

can have a different profit than going from city j to city i.  

After there will be a line with E integers, the identifier of the cities he can end his tour.  

Output

For each input case produce one line of output, the total profit he can earn in the corresponding tour.  

Sample Input

1 

 3 1 2 2 

 0 3 5

 5 0 1 

 9 2 0

 2 3

Sample Output

7