A transit map has n stations connected by two-way corridors. Every corridor takes exactly one hop to traverse. Given a start station and a destination station, determine the minimum number of hops needed to travel from start to destination.

If the destination cannot be reached from the start, report -1. If the start and destination are the same station, the answer is 0.

Input format

Line 1: two integers n and m — the number of stations and the number of corridors. Next m lines: two integers u v (0-indexed) meaning there is a two-way corridor between station u and station v. Last line: two integers s t — the start station and the destination station.

Output format

A single integer: the minimum number of hops from s to t, or -1 if t is unreachable from s.

Constraints

• 1 \u2264 n \u2264 100000
• 0 \u2264 m \u2264 200000
• 0 \u2264 u, v, s, t < n
• There are no self-loops. There may be at most one corridor between any pair of stations.

4 4
0 1
1 3
0 2
2 3
0 3

2

5 2
0 1
2 3
0 4

-1