Given a connected graph \(G\) with \(N\) nodes and \(M\) edges (edges are bi-directional). Every node is assigned a value \(A[i]\). We define a value of a simple path as :

• Value of path = Maximum of (absolute difference between values of adjacent nodes in a path).

A path consists of a sequence of nodes starting with start node \(S\) and end node \(E\). 

• \(S - u_1 - u_2 - .... - E\) is a simple path if all nodes on the path are distinct and  \(S, u_1, u_2, ..., E\) are nodes in \(G\).

Given a start node \(S\) and end node \(E\), find the minimum possible "value of path" which starts with node \(S\) and ends with node \(E\).

Input format

• First line contains two space-separated integers \(N \ M\)
• Second line contains two space-separated integers \(S \ E\)
• Next M lines contain two space-separated integers u v, denoting an edge between node u and v
• Next line contains \(N\) space-separated integers denoting values of nodes.

Output format

Print a single integer — minimum possible "value of path" between node \(S\) and \(E\).

Constraints

\(1 \le N \le 10^5 \\ N - 1 \le M \le 10^6 \\ \\ 1 \leq S, E \leq N \\ S \neq E \\ \\ 1 \leq u, v \leq N \\ 1 \le A[i] \le 10^6\)