Problem: Soon there will be held the world's largest programming contest, but the testing system still has m bugs. The contest organizer, a well-known university, has no choice but to attract university students to fix all the bugs. The university has n students able to perform such work. The students realize that they are the only hope of the organizers, so they don't want to work for free: the i-th student wants to get ci 'passes' in his subjects (regardless of the volume of his work).

Bugs, like students, are not the same: every bug is characterized by complexity aj, and every student has the level of his abilities bi. Student i can fix a bug j only if the level of his abilities is not less than the complexity of the bug: bi ≥ aj, and he does it in one day. Otherwise, the bug will have to be fixed by another student. Of course, no student can work on a few bugs in one day. All bugs are not dependent on each other, so they can be corrected in any order, and different students can work simultaneously.

The university wants to fix all the bugs as quickly as possible, but giving the students the total of not more than s passes. Determine which students to use for that and come up with the schedule of work saying which student should fix which bug.

Input

The first line contains three space-separated integers: n, m and s (1 ≤ n, m ≤ 105, 0 ≤ s ≤ 109) — the number of students, the number of bugs in the system and the maximum number of passes the university is ready to give the students.

The next line contains m space-separated integers a1, a2, ..., am (1 ≤ ai ≤ 109) — the bugs' complexities.

The next line contains n space-separated integers b1, b2, ..., bn (1 ≤ bi ≤ 109) — the levels of the students' abilities.

The next line contains n space-separated integers c1, c2, ..., cn (0 ≤ ci ≤ 109) — the numbers of the passes the students want to get for their help.

Output

If the university can't correct all bugs print "NO".

Otherwise, on the first line print "YES", and on the next line print m space-separated integers: the i-th of these numbers should equal the number of the student who corrects the i-th bug in the optimal answer. The bugs should be corrected as quickly as possible (you must spend the minimum number of days), and the total given passes mustn't exceed s. If there are multiple optimal answers, you can output any of them.

Examples

Input

3 4 9
1 3 1 2
2 1 3
4 3 6


Output

YES
2 3 2 3


Input

3 4 10
2 3 1 2
2 1 3
4 3 6


Output

YES
1 3 1 3


Input

3 4 9
2 3 1 2
2 1 3
4 3 6


Output

YES
3 3 2 3


Input

3 4 5
1 3 1 2
2 1 3
5 3 6


Output

NO

Note

Consider the first sample.

The third student (with level 3) must fix the 2nd and 4th bugs (complexities 3 and 2 correspondingly) and the second student (with level 1) must fix the 1st and 3rd bugs (their complexity also equals 1). Fixing each bug takes one day for each student, so it takes 2 days to fix all bugs (the students can work in parallel).

The second student wants 3 passes for his assistance, the third student wants 6 passes. It meets the university's capabilities as it is ready to give at most 9 passes.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class B2 {
    public static long time = 0;

    public static void main(String[] args) throws Exception {
        time = System.currentTimeMillis();
        solve();
        out.flush();
    }
    static final int LIM = 100000 + 10;
    static final int[] complexities = new int[LIM];
    static final int[] skills = new int[LIM];
    static final int[] costs = new int[LIM];
    static int studentno= -1, bugno = -1, s1 = -1;
    static int[] fin = new int[LIM];
    public static int[] check(int maxday, Integer[] order){
        PriorityQueue<Integer> canuse = new PriorityQueue(10, new Comparator<Integer>(){
            @Override
            public int compare(Integer o1, Integer o2) {
                return costs[o1] - costs[o2];
            }
        });
        long usedcost = 0;
        int includedStudent = 0;
        for (int i = 0; i < bugno; i+=maxday){
//          px(i, usedcost , "used");
            for (;;){
                if (includedStudent >= studentno) break;
                
                int id = order[includedStudent];
                int skill = skills[id];
//              px(skill, complexities[i], ptr);
                if (skill >= complexities[i]){
                    canuse.add(id);
                    includedStudent++;
                }
                else break;
            }
//          px(canuse.size());
//          for (int[] e: canuse) p(Arrays.toString(e));
//          pn("done queue");
            for (;;){
//              for (int[] e: canuse) p(Arrays.toString(e));
//              pn("done queue");
                if (canuse.size() <= 0){
                    
                    return null;
                }
                int best = canuse.poll();
                
                for (int j =0; j < maxday; j++){
                    if (i + j >= bugno) break;
                    fin[i + j] = best;
                }
//              px(maxday,Arrays.copyOf(fin, m1));
                int cost = costs[best];
                usedcost += cost;
                break;
            }
        }
        long remain = s1;
        remain -= usedcost;
//      px("query",maxday, usedcost, s1);
        if (remain >=0) return fin;
        return null;
    }
    public static void solve() throws Exception {
        studentno = ni();
        bugno = ni();
        s1 = ni();
        

        for (int i =0; i < bugno; i++){
            complexities[i] = ni();
        }
        Integer[] oldorder = new Integer[bugno];
        for (int i = 0; i < bugno; i++){
            oldorder[i] = i;
        }
        Arrays.sort(oldorder, new Comparator<Integer>() {
            @Override
            public int compare(Integer o1, Integer o2) {
                return -(complexities[o1] - complexities[o2]);
            }
        });
//      px(oldorder);
        int[] reverse = new int[bugno];
        for (int i =0; i < bugno; i++){
            reverse[oldorder[i]] = i;
        }
        
        
        Arrays.sort(complexities, 0, bugno);
        for (int i =0; i < bugno/2; i++){
            int temp = complexities[i];
            complexities[i] = complexities[bugno -1 - i];
            complexities[bugno -1 - i] = temp;
        }
//      px(Arrays.copyOf(complexities, m1));
        for (int i =0; i < studentno; i++){
            skills[i] = ni();
        }
        for (int i =0; i < studentno; i++){
            costs[i] = ni();
        }
        Integer[] order = new Integer[studentno];
        for (int i =0; i < studentno; i++) order[i] = i;
        Arrays.sort(order, new Comparator<Integer>(){
            @Override
            public int compare(Integer q1, Integer q2) {
                if (skills[q1] != skills[q2]){
                    return -(skills[q1] - skills[q2]);
                }
                return (costs[q1] - costs[q2]);
            }
        });
//      for (int e: order){
//          px(skills[e], costs[e]);
//      }
        
//      for (int i =0; i < m1; i++){
//          px(i,"day",check(i, order) != null);
//      }
        
        if (check(bugno, order) == null){
            pn("NO");
            return;
        }
        int low = 1;
        int high = bugno;
        for (;high - low > 1;){
            int mid = (low + high)/2;
            if (check(mid, order) != null){
                high = mid;
            }
            else {
                low = mid;
            }
        }
//      px(check(low, order) == null);
        if (check(low, order) != null){
            
        }
        else {
            check(high, order);
        }
        pn("YES");
//      px(reverse);
        p(fin[reverse[0]] + 1);
        for (int i =1; i < bugno; i++){
            p(" "+(fin[reverse[i]]+1));
        }
        pn();
    }

    public static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    public static StringTokenizer st = null;

    public static String nx() throws Exception {
        for (; st == null || !st.hasMoreTokens();) {
            String k1 = in.readLine();
            if (k1 == null) return null;
            st = new StringTokenizer(k1);
        }
        return st.nextToken();
    }

    public static int ni() throws Exception {
        return Integer.parseInt(nx());
    }

    public static long nl() throws Exception {
        return Long.parseLong(nx());
    }

    public static double nd() throws Exception {
        return Double.parseDouble(nx());
    }

    public static void px(Object... l1) {
        System.out.println(Arrays.deepToString(l1));
    }

    public static boolean FLUSH = false;
    public static PrintWriter out = new PrintWriter(System.out, FLUSH);

    public static void p(Object... l1) {
        for (int i = 0; i < l1.length; i++) {
            if (i != 0) out.print(' ');
            out.print(l1[i].toString());
        }
    }

    public static void pn(Object... l1) {
        for (int i = 0; i < l1.length; i++) {
            if (i != 0) out.print(' ');
            out.print(l1[i].toString());
        }
        out.println();
    }

    public static void pn(Collection l1) {
        boolean first = true;
        for (Object e : l1) {
            if (first) first = false;
            else out.print(' ');
            out.print(e.toString());
        }
        out.println();
    }

}