Jumps in pairs S97190

Given an undirected graph and two vertices s and t, compute the minimum number of jumps needed to go from s to t. Here, we say that a jump between two vertices x and z is possible if there is a vertex y adjacent to both x and z.

Input

Input consists of several graphs. Every case begins with n, m, s and t, followed by m pairs x ‍y, with x ≠ y, indicating an edge between x and y. Suppose 2 ≤ n ≤ 10⁵, 0 ≤ m ≤ 5n, s ≠ t, that the vertices are numbered between 0 and n − 1, and that there are no repeated edges.

Output

For each graph, print the minimum number of jumps to go from s to t. If it is impossible, print “NO”.

Observation

Even if a green light is obtained, only Θ(n+m) solutions will receive the maximum score.