The cows have been sent on a mission through space to acquire a new milking machine for their barn. They are flying through a cluster of stars containing $N$ ($1 \le N \le 50{,}000$) planets, each with a trading post.

The cows have determined which of $K$ ($1 \le K \le 1{,}000$) types of objects (numbered $1..K$) each planet in the cluster desires, and which products they have to trade. No planet has developed currency, so they work under the barter system: all trades consist of each party trading exactly one object (presumably of different types).

The cows start from Earth with a canister of high quality hay (item 1), and they desire a new milking machine (item $K$). Help them find the best way to make a series of trades at the planets in the cluster to get item $K$. If this task is impossible, output -1.

Input

• Line 1: Two space-separated integers, $N$ and $K$.
• Lines $2..N+1$: Line $i+1$ contains two space-separated integers, $a_i$ and $b_i$ respectively, that are planet $i$'s trading trading products. The planet will give item $b_i$ in order to receive item $a_i$.

Output

• Line 1: One more than the minimum number of trades to get the milking machine which is item $K$ (or -1 if the cows cannot obtain item $K$).
• Lines $2..T+1$: The ordered list of the objects that the cows possess in the sequence of trades.

Examples

Input 1

6 5
1 3
3 2
2 3
3 1
2 5
5 4

Output 1

4
1
3
2
5

Output Details

The cows possess 4 objects in total: first they trade object 1 for object 3, then object 3 for object 2, then object 2 for object 5.

Problem credits: Coaches, 2004