Taco: Shortest Delay

You are given a network of N servers and M communication links. Each link connects two servers and has an associated delay. However, only the links with delay not exceeding a given threshold K can be used.

Your task is to compute the minimum total delay required to send data from a source server S to a target server T. Formally, if a link connects servers A_i and B_i with delay D_i, it can be used only if
\( D_i \le K \).

If there exists no valid path from S to T following the constraint, output -1.

Hint: You may use Dijkstra's algorithm to solve this problem efficiently, considering only the allowed links.

inputFormat

The first line contains five integers: N M S T K, where:

• N is the number of servers.
• M is the number of communication links.
• S is the source server.
• T is the target server.
• K is the maximum allowed delay for a link to be used.

Each of the following M lines contains three integers: Ai Bi Di, where the link connects server Ai to server Bi with a delay of Di.

outputFormat

Output a single integer – the minimum total delay to send data from server S to server T using only links with delay \( \le K \). If it is impossible, output -1.

4 5 1 4 3
1 2 2
2 3 1
3 4 2
1 3 5
2 4 4

5