Time Limit:3000ms Memory Limit:65536KB
Description
Farmer John dutifully checks on the cows every day. He traverses
some of the M (1 <= M <= 50,000) trails conveniently numbered 1..M
from pasture 1 all the way out to pasture N (a journey which is
always possible for trail maps given in the test data). The N (1
<= N <= 10,000) pastures conveniently numbered 1..N on Farmer John's
farm are currently connected by bidirectional dirt trails.  Each
trail i connects pastures P1_i and P2_i (1 <= P1_i <= N; 1 <= P2_i
<= N) and requires T_i (1 <= T_i <= 1,000,000) units of time to
traverse.

He wants to revamp some of the trails on his farm to save time on
his long journey. Specifically, he will choose K (1 <= K <= 20)
trails to turn into highways, which will effectively reduce the
trail's traversal time to 0. Help FJ decide which trails to revamp
to minimize the resulting time of getting from pasture 1 to N.

Input
* Line 1: Three space-separated integers: N, M, and K

* Lines 2..M+1: Line i+1 describes trail i with three space-separated
        integers: P1_i, P2_i, and T_i


Output
* Line 1: The length of the shortest path after revamping no more than
        K edges

Sample Input
4 4 1
1 2 10
2 4 10
1 3 1
3 4 100
Sample Output
1
Hint
OUTPUT DETAILS:

K is 1; revamp trail 3->4 to take time 0 instead of 100. The new shortest
path is 1->3->4, total traversal time now 1.