## UTS Open '15 #5 - Distribution Channel

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Points: 17 (partial)
Time limit: 3.0s
Memory limit: 256M

Author:
Problem types
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Distribution channels are often very confusing.

After acquiring enough funding and finally finishing the development for her product, Mrs. Evans wants to release it to the local market. However, the Canadian Competition Act prevents her from choosing the cheapest way to connect her stores.

In order to spend the least amount of money and abide to the Canadian Competition Act, she must find the second cheapest way to connect her stores.

Mrs. Evans hopes to open () stores and there are () possible connections between her stores. The connection connects station to station with a cost of . She can only choose connections.

If it is impossible for her to do this, output .

N.B. The time limit is rather strict for certain slow languages like Python and Java. C++ is recommended for this question.

#### Partial Marks

For 25% of the marks, you may assume that , .

For 50% of the marks, you may assume that , .

#### Input Format

The first line will contain , and . The of the next lines will contain , , and , where ().

#### Output Format

A single line containing the second cheapest way to connect her stores.

#### Sample Input 1

3 3
1 2 1
2 3 2
3 1 3

#### Sample Output 1

4

#### Explanation

Mrs. Evans chooses the following connections for a total cost of :

• with cost
• with cost

#### Sample Input 2

5 10
2 3 5
1 5 5
1 2 3
1 3 2
5 3 2
4 3 3
4 5 9
4 2 10
5 2 4
4 1 9

#### Sample Output 2

11

#### Explanation

Mrs. Evans chooses the following connections for a total cost of :

• with cost
• with cost
• with cost
• with cost

• commented on Aug. 10, 2015, 8:32 p.m. edit 2

Mod edit: image way too large.

http://i.imgur.com/A0Bx3CN.png

Me edit: The problem is fixed, you can submit now.

• commented on Feb. 11, 2015, 4:59 p.m.

"If it is possible for her to do this, output −1."

• commented on Feb. 11, 2015, 5:02 p.m.

What if there are multiple ways of connecting the stores as cheaply as possible? Is the second-cheapest option then equal in cost to the cheapest option? Or do we find the cheapest option with a larger cost?

• commented on Feb. 11, 2015, 5:11 p.m.

Sorry it was a typo, and it is the cheapest option with a larger cost.

• commented on Feb. 11, 2015, 4:47 p.m.

When you say if it is possible, I think you mean the opposite.

• commented on Feb. 11, 2015, 4:48 p.m.

Relevant: In re Sample Input 2, CAN IT BE?