Problem 23831 --Remmarguts' Date(poj 2449)

23831: Remmarguts' Date(poj 2449)

Time Limit: 1 Sec  Memory Limit: 128 MB
Submit: 192  Solved: 68
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"Good man never makes girls wait or breaks an appointment!" said the mandarin duck father. Softly touching his little ducks' head, he told them a story. 

"Prince Remmarguts lives in his kingdom UDF – United Delta of Freedom. One day their neighboring country sent them Princess Uyuw on a diplomatic mission." 

"Erenow, the princess sent Remmarguts a letter, informing him that she would come to the hall and hold commercial talks with UDF if and only if the prince go and meet her via the K-th shortest path. (in fact, Uyuw does not want to come at all)" 

Being interested in the trade development and such a lovely girl, Prince Remmarguts really became enamored. He needs you - the prime minister's help! 

DETAILS: UDF's capital consists of N stations. The hall is numbered S, while the station numbered T denotes prince' current place. M muddy directed sideways connect some of the stations. Remmarguts' path to welcome the princess might include the same station twice or more than twice, even it is the station with number S or T. Different paths with same length will be considered disparate. 




* 第1行: n,m(1 <= N <= 1000, 0 <= M <= 10000).车站的编号从1到n
* 第2到1+M行: 第i+1行表示第i条单向向道路,包含两个由空格隔开的整数: A_i和B_i以及它们之间的路径长度t(1<=t<=100)
*最后一行是s,t,k(1 <= S, T <= N, 1 <= K <= 1000)



Sample Input

2 2
1 2 5
2 1 4
1 2 2

Sample Output