Given a connected, undirected graph $G$ with $N$ nodes and $M$ edges. Every node has a value assigned to it, denoted by the array $A$.

An edge $E$ is said to be special iff :

• There exists at least one pair $(u, v), u < v$ such that any simple path between node $u$ and $v$ will always include the edge $E$. 
• The strength of such an edge is defined as $\sum A[u] \times A[v]$ over all such pairs.

Among all the special edges, find the special edge with the maximum strength in the graph.

If there exists more than one answer, suppose edge $E (a, b)$ and $E'(a',b')$ where $a < b \ \& \ a' < b'$

• Return the edge with smaller node as the first value in the pair i.e. $a, a'$
• If, there still exists more than one answer, return the edge with smaller node as the second value in the pair i.e. $b, b'$

If there does not exists any such edge, return pair $(n+1, n+1)$

Input format

• First line contains two space-separated integers $N, M$
• Next line contains $N$ space-separated integers denoting the array A.
• Next $M$ lines contains two space-separated integers denoting an edge.

Output format

Print two space-separated integers $a \ b$, denoting the special edge with maximum strength. Please note $a < b$

Constraints

$1 \le N, M\le 10^5 \\ 1 \le A[i] \le 10^4$