I didn't understand this solution to Synchronous Shopping on hackerrank

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I have tried those days to solve this hackerrank challenge Synchronous Shopping | HackerRank but when I’ve seen the solution I didn’t understand it, the are using bitwise operations and the problem I didn’t know the logic and the proof behind using them, I have here a solution if anyone can explain me them, it’ll be very helpful, here’s the code in java :

import java.io.;
import java.util.;

public class Solution {
static class Node {
int label, time, status;
public Node(int label, int time, int status) {
this.label = label;
this.time = time;
this.status = status;
}
}

private static int minTime(int n, int k, int[] sale, List<List<Node>> graph) {
    int[][] time = new int[1 << k][n];
    for (int[] t : time) Arrays.fill(t, Integer.MAX_VALUE);
    PriorityQueue<Node> minHeap = new PriorityQueue<>(new Comparator<Node>(){
        @Override
        public int compare(Node n1, Node n2) {
            return n1.time - n2.time;
        }
    });
    minHeap.offer(new Node(0, 0, sale[0]));
    time[sale[0]][0] = 0;
    List<Node> candidates = new ArrayList<>();
    while (!minHeap.isEmpty()) {
        Node cur = minHeap.poll();
        if (cur.label == n - 1) candidates.add(cur);
        for (Node node : graph.get(cur.label)) {
            int newStatus = (cur.status | sale[node.label]);
            if (cur.time + node.time < time[newStatus][node.label]) {
                time[newStatus][node.label] = cur.time + node.time;
                minHeap.offer(new Node(node.label, cur.time + node.time, newStatus));
            }
        }
    }

    int min = Integer.MAX_VALUE;
    for (int i = 0; i < candidates.size(); i++) {
        Node cur = candidates.get(i);
        for (int j = i; j < candidates.size(); j++) {
            Node another = candidates.get(j);
            if ((cur.status | another.status) == (1 << k) - 1) {
                min = Math.min(min, Math.max(cur.time, another.time));
            }
        }
    }
    return min;
}

private static final Scanner SCANNER = new Scanner(System.in);

public static void main(String[] args) {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT. Your class should be named Solution. */
    String nmk = SCANNER.nextLine();
    String[] nmkVals = nmk.split(" ");
    int n = Integer.valueOf(nmkVals[0]), m = Integer.valueOf(nmkVals[1]), k = Integer.valueOf(nmkVals[2]);

    int[] sale = new int[n];
    for (int i = 0; i < n; i++) {
        String items = SCANNER.nextLine();
        String[] types = items.split(" ");
        for (int j = 1; j < types.length; j++) {
            sale[i] |= (1 << (Integer.valueOf(types[j]) - 1));
        }
    }

    List<List<Node>> graph = new ArrayList<>();
    for (int i = 0; i < n; i++) graph.add(new ArrayList<>());
    for (int i = 0; i < m; i++) {
        String edge = SCANNER.nextLine();
        String[] detail = edge.split(" ");
        int n1 = Integer.valueOf(detail[0]) - 1, n2 = Integer.valueOf(detail[1]) - 1, t = Integer.valueOf(detail[2]);
        graph.get(n1).add(new Node(n2, t, 0));
        graph.get(n2).add(new Node(n1, t, 0));
    }

    System.out.print(minTime(n, k, sale, graph));
}

}