# [Usaco2005 feb]Secret Milking Machine 神秘的挤奶机

### 题目描述

Farmer John is constructing a new milking machine and wishes to keep it secret as long as possible. He has hidden in it deep within his farm and needs to be able to get to the machine without being detected. He must make a total of T (1 <= T <= 200) trips to the machine during its construction. He has a secret tunnel that he uses only for the return trips. The farm comprises N (2 <= N <= 200) landmarks (numbered 1..N) connected by P (1 <= P <= 40,000) bidirectional trails (numbered 1..P) and with a positive length that does not exceed 1,000,000. Multiple trails might join a pair of landmarks. To minimize his chances of detection, FJ knows he cannot use any trail on the farm more than once and that he should try to use the shortest trails. Help FJ get from the barn (landmark 1) to the secret milking machine (landmark N) a total of T times. Find the minimum possible length of the longest single trail that he will have to use, subject to the constraint that he use no trail more than once. (Note well: The goal is to minimize the length of the longest trail, not the sum of the trail lengths.) It is guaranteed that FJ can make all T trips without reusing a trail.

### 输入格式

* Line 1: Three space-separated integers: N, P, and T * Lines 2..P+1: Line i+1 contains three space-separated integers, A_i, B_i, and L_i, indicating that a trail connects landmark A_i to landmark B_i with length L_i.

第1行是3个整数N、P和T，用空格隔开．
第2到P+1行，每行包括3个整数，Ai，Bi，Li．表示区域Ai、Bi之间有一条长度为Li的道路．

### 输出格式

* Line 1: A single integer that is the minimum possible length of the longest segment of Farmer John's route.

输出只有一行，包含一个整数，即约翰经过的这些道路中最长的路的最小长度．

```7 9 2
1 2 2
2 3 5
3 7 5
1 4 1
4 3 1
4 5 7
5 7 1
1 6 3
6 7 3
```

```5

Gold