**Time limit:**1.00 s**Memory limit:**512 MB

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