## CCC '15 S4 - Convex Hull

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Points: 15 (partial)
Time limit: 5.0s
Memory limit: 512M

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Problem type
##### Canadian Computing Competition: 2015 Stage 1, Senior #4

You are travelling on a ship in an archipelago. The ship has a convex hull which is centimetres thick. The archipelago has islands, numbered from to . There are sea routes amongst them, where the route runs directly between two different islands and ; , takes minutes to travel along in either direction, and has rocks that wear down the ship's hull by centimetres. There may be multiple routes running between a pair of islands.

You would like to travel from island to a different island along a sequence of sea routes, such that your ship's hull remains intact – in other words, such that the sum of the routes' values is strictly less than .

Additionally, you are in a hurry, so you would like to minimize the amount of time necessary to reach island from island . It may not be possible to reach island from island , however, either due to insufficient sea routes or the having the ship's hull wear out.

#### Input Specification

The first line of input contains three integers , and , each separated by one space.

The next lines each contain integers , , and , each separated by one space. The line in this set of lines describes the sea route (which runs from island to island , takes minutes and wears down the ship's hull by centimetres). Notice that (that is, the ends of a sea route are distinct islands).

The last line of input contains two integers and , the islands between which we want to travel.

For 20% of marks for this question, and . For another 20% of the marks for this problem, and .

#### Output Specification

Output a single integer: the integer representing the minimal time required to travel from to without wearing out the ship's hull, or -1 to indicate that there is no way to travel from to without wearing out the ship's hull.

#### Sample Input 1

10 4 7
1 2 4 4
1 3 7 2
3 1 8 1
3 2 2 2
4 2 1 6
3 4 1 1
1 4 6 12
1 4

#### Output for Sample Input 1

7

#### Explanation of Output for Sample Input 1

The path of length from to would wear out the hull of the ship. The three paths of length ( and two different ways) take at least minutes but wear down the hull too much. The path takes minutes and only wears down the hull by centimetres, whereas the path takes minutes and wears down the hull by centimetres.

#### Sample Input 2

3 3 3
1 2 5 1
3 2 8 2
1 3 1 3
1 3

#### Output for Sample Input 2

-1

#### Explanation of Output for Sample Input 2

The direct path wears down the hull to , as does the path .