Secret Milking Machine   (secret.X) 

Farmer Mike 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, FM knows he cannot use any
trail on the farm more than once and that he should try to use the
shortest trails.

Help FM 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 used, not the sum of the
trail lengths.)

It is guaranteed that FM can make all T trips without reusing a trail.

PROBLEM NAME: secret

INPUT FORMAT:

* 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.

SAMPLE INPUT:

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

OUTPUT FORMAT:

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

SAMPLE OUTPUT:

5

OUTPUT DETAILS:

Farmer Mike can travel trails 1 - 2 - 3 - 7 and 1 - 6 - 7.  None of
the trails travelled exceeds 5 units in length.  It is impossible
for Farmer Mike to travel from 1 to 7 twice without using at least
one trail of length 5.