/* package whatever; // don't place package name! */
 
import java.util.*;
import java.lang.*;
import java.io.*;
 
/* Name of the class has to be "Main" only if the class is public. */
class Ideone
{
	public static void main(String[] args) {
        final List<Integer> path = solve(3, 6, 4, 1, 3, 4, 2, 5, 3, 0);
 
        for (Integer i : path) {
            System.out.print(i + " -> ");
        }
        System.out.println("DONE");
    }
 
    static List<Integer> solve(int... a) {
        //Value in each element is the index, from where we can come here
        int[] path = new int[a.length];
        Arrays.fill(path, -1); //No index is accessible yet
 
        //Queue of positions that were visited from somewhere, but nothing was tried to be 
        //visited from them. At the beginning, 0 is in the list, because it's starting point.
        //Then, if we visit index 3, it is added to this list for later processing.
        Queue<Integer> posQueue = new LinkedList<>();
        posQueue.add(0);
        path[0] = 0; //0 index is accessible from itself, this is starting position
 
        while (!posQueue.isEmpty()) {
            int pos = posQueue.remove();
            int prPos = pos - a[pos];
            int nxPos = pos + a[pos];
            if (prPos >= 0 && path[prPos] == -1) {
                path[prPos] = pos;
                posQueue.add(prPos);
            }
            if (nxPos < a.length && path[nxPos] == -1) {
                path[nxPos] = pos;
                posQueue.add(nxPos);
            }
 
            if (path[a.length-1] != -1) {
                break;
            }
        }
 
        if (path[a.length-1] == -1) {
            return null;
        }
 
        //Collect the path
        List<Integer> result = new ArrayList<>();
        int idx = a.length-1;
        while (idx != 0) {
            result.add(0, idx);
            idx = path[idx];
        }
        result.add(0, 0);
        return result;
    }
}

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