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

A game consists of n rooms and m teleporters. At the beginning of each day, you start in room 1 and you have to reach room n.

You can use each teleporter at most once during the game. You want to play the game for exactly k days. Every time you use any teleporter you have to pay one coin. What is the minimum number of coins you have to pay during k days if you play optimally?

# Input

The first input line has three integers n, m and k: the number of rooms, the number of teleporters and the number of days you play the game. The rooms are numbered 1,2,\dots,n.

After this, there are m lines describing the teleporters. Each line has two integers a and b: there is a teleporter from room a to room b.

There are no two teleporters whose starting and ending room are the same.

# Output

First print one integer: the minimum number of coins you have to pay if you play optimally. Then, print k route descriptions according to the example. You can print any valid solution.

If it is not possible to play the game for k days, print only -1.

# Constraints

- 2 \le n \le 500
- 1 \le m \le 1000
- 1 \le k \le n-1
- 1 \le a,b \le n

# Example

Input:

8 10 2 1 2 1 3 2 5 2 4 3 5 3 6 4 8 5 8 6 7 7 8

Output:

6 4 1 2 4 8 4 1 3 5 8