Note: This is an approximate problem. There is no exact solution. You must find the most optimal solution. Please, take a look at the sample explanation to ensure that you understand the problem correctly.

Problem statement

Given an undirected graph of N nodes and M edges. Every node has a weight attached to it denoted by an array W. 

Select a subset of nodes say S, such that for every edge (u,v) in the above graph there exists either u or v in the subset S.

Let's define weight of set S as X = $|S| \times \sum{W[i]}$, where $i$ denotes all the nodes present in the subset S and $|S|$ denotes size of subset.

Aim is to minimize X.

Note:

• Calculation of X, will only include distinct elements from the subset, even if it contains duplicate elements.

Input format :

• First line contains two space-separated integers : N and M 
• Second line contain N space-separated integers denoting the array W.
• Next M lines contains two space-separated integers u v, denoting an edge between node u and v.

Output format :

• In the first line print an integer denoting the size of the second say Y (maximum value can be N).
• In the next line print Y space separated integers denoting the nodes present in the subset.

Verdict and scoring :

• Your score is equal to the sum of the values of all test files. The value of each test file is equal to the value of X that you found.

  If the subset is invalid you will receive a wrong answer verdict.

Constraints :

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