Jumps in pairs

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 $x \ne y$ , indicating an edge between $x$ and $y$ . Suppose $2 \le n \le 10^5$ , $0 \le m \le 5n$ , $s \ne t$ , 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 $\Theta(n+m)$ solutions will receive the maximum score.

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T12:49:45.211Z