Graph Paths II

Consider a directed weighted graph having n nodes and m edges. Your task is to calculate the minimum path length from node 1 to node n with exactly k edges.

Input

The first input line contains three integers n, m and k: the number of nodes and edges, and the length of the path. The nodes are numbered 1,2,\dots,n. Then, there are m lines describing the edges. Each line contains three integers a, b and c: there is an edge from node a to node b with weight c.

Output

Print the minimum path length. If there are no such paths, print -1.

Constraints

$1 \le n \le 100$

$1 \le m \le n(n-1)$

$1 \le k \le 10^9$

$1 \le a,b \le n$

$1 \le c \le 10^9$

Example

Input

3 4 8
1 2 5
2 3 4
3 1 1
3 2 2

Output

27