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.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * 4 4
 * 1 5 3 4
 * 1 2
 * 1 3
 * 2 3
 * 3 3
 *
 *
 * @author pttrung
 */
public class A {

    public static long Mod = (long) (1e9);
    public static int[][][] dp;

    public static void main(String[] args) throws FileNotFoundException {

        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        int n = in.nextInt();
        int m = in.nextInt();
        int s = in.nextInt();
        Bug[] bs = new Bug[m];
        Student[] st = new Student[n];
        int max = 0;
        int end = m;
        int result = -1;
        for (int i = 0; i < m; i++) {
            bs[i] = new Bug(in.nextInt(), i);
        }
        for (int i = 0; i < n; i++) {
            st[i] = new Student(in.nextInt(), 0, i);
        }
        for (int i = 0; i < n; i++) {
            st[i].pas = in.nextInt();

        }

        Arrays.sort(bs);
        Arrays.sort(st);
        int start = 0;
        while (start <= end) {
            int mid = (start + end) / 2;
            int i = m - 1;
            int stu = n - 1;
            PriorityQueue<Student> q = new PriorityQueue(n, new Comparator<Student>() {

                @Override
                public int compare(Student o1, Student o2) {
                    return o1.pas -o2.pas;
                }
            });
            int left = s;
            boolean[] check = new boolean[n];

            while (i >= 0 && left >= 0) {
                while(stu >= 0 && st[stu].ab >= bs[i].dif){
                    q.add(st[stu--]);
                    
                    
                }
                if(q.isEmpty()){
                    break;
                }else{
                  Student a =  q.poll();
                  left -= a.pas;
                }

                i -= mid;
            }
            if (i >= 0 || left < 0) {
                start = mid + 1;
            } else {
                end = mid - 1;
                if (result == -1 || result > mid) {
                    result = mid;
                }
            }
        }
        if (result == -1) {
            out.println("NO");
        } else {
           // System.out.println(result);
            out.println("YES");
            int[] res = new int[m];
            int i = m - 1;
            int left = s;
            int stu = n - 1;
            PriorityQueue<Student> q = new PriorityQueue(n, new Comparator<Student>() {

                @Override
                public int compare(Student o1, Student o2) {
                    return o1.pas -o2.pas;
                }
            });
            

            while (i >= 0 && left >= 0) {
               while(stu >= 0 && st[stu].ab >= bs[i].dif){
                    q.add(st[stu--]);
                    
                    
                }
                if(q.isEmpty()){
                    break;
                }else{
                  Student a =  q.poll();
                  for(int j = i; j >= Math.max(0, i - result + 1); j--){
                      res[bs[j].index] = a.index;
                  }
                }

                i -= result;
            }
            for (int j = 0; j < m; j++) {
                out.print((res[j] + 1) + " ");
            }

        }


        out.close();
    }

    static class Bug implements Comparable<Bug> {

        int dif, index;

        public Bug(int dif, int index) {
            this.dif = dif;
            this.index = index;
        }

        @Override
        public int compareTo(Bug o) {
            return dif - o.dif;
        }
    }

    static class Student implements Comparable<Student> {

        int ab, pas, index;

        public Student(int ab, int pas, int index) {
            this.ab = ab;
            this.pas = pas;
            this.index = index;
        }

        @Override
        public int compareTo(Student o) {
            
            return ab - o.ab;
        }
    }

    static int find(int index, int[] u) {
        if (index != u[index]) {
            return u[index] = find(u[index], u);
        }
        return index;
    }

    public static long pow(int a, int b, long mod) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long v = pow(a, b / 2, mod);
        if (b % 2 == 0) {
            return (v * v) % mod;
        } else {
            return (((v * v) % mod) * a) % mod;
        }
    }

    public static int[][] powSquareMatrix(int[][] A, long p) {
        int[][] unit = new int[A.length][A.length];
        for (int i = 0; i < unit.length; i++) {
            unit[i][i] = 1;
        }
        if (p == 0) {
            return unit;
        }
        int[][] val = powSquareMatrix(A, p / 2);
        if (p % 2 == 0) {
            return mulMatrix(val, val);
        } else {
            return mulMatrix(A, mulMatrix(val, val));
        }

    }

    public static int[][] mulMatrix(int[][] A, int[][] B) {
        int[][] result = new int[A.length][B[0].length];
        for (int i = 0; i < result.length; i++) {
            for (int j = 0; j < result[0].length; j++) {
                long temp = 0;
                for (int k = 0; k < A[0].length; k++) {

                    temp += ((long) A[i][k] * B[k][j] % Mod);
                    temp %= Mod;
                }
                temp %= Mod;
                result[i][j] = (int) temp;
            }
        }

        return result;
    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;




    }

    static class FT {

        int[] data;

        FT(int n) {
            data = new int[n];
        }

        void update(int index, int val) {
            // System.out.println("UPDATE INDEX " + index);
            while (index < data.length) {
                data[index] += val;
                index += index & (-index);

                //    System.out.println("NEXT " +index);
            }
        }

        int get(int index) {
            //  System.out.println("GET INDEX " + index);
            int result = 0;
            while (index > 0) {
                result += data[index];
                index -= index & (-index);
                // System.out.println("BACK " + index);
            }
            return result;
        }
    }

    static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        } else {
            return gcd(b, a % b);
        }
    }

    static long pow(long a, int b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {

            return val * val % Mod;
        } else {
            return (val * val % Mod) * a % Mod;
        }
    }

//    static Point intersect(Point a, Point b, Point c) {
//        double D = cross(a, b);
//        if (D != 0) {
//            return new Point(cross(c, b) / D, cross(a, c) / D);
//        }
//        return null;
//    }
//
//    static Point convert(Point a, double angle) {
//        double x = a.x * cos(angle) - a.y * sin(angle);
//        double y = a.x * sin(angle) + a.y * cos(angle);
//        return new Point(x, y);
//    }
    static Point minus(Point a, Point b) {
        return new Point(a.x - b.x, a.y - b.y);
    }
//
//    static Point add(Point a, Point b) {
//        return new Point(a.x + b.x, a.y + b.y);
//    }
//

    /**
     * Cross product ab*ac
     *
     * @param a
     * @param b
     * @param c
     * @return
     */
    static double cross(Point a, Point b, Point c) {
        Point ab = new Point(b.x - a.x, b.y - a.y);
        Point ac = new Point(c.x - a.x, c.y - a.y);
        return cross(ab, ac);
    }

    static double cross(Point a, Point b) {
        return a.x * b.y - a.y * b.x;
    }

    /**
     * Dot product ab*ac;
     *
     * @param a
     * @param b
     * @param c
     * @return
     */
    static long dot(Point a, Point b, Point c) {
        Point ab = new Point(b.x - a.x, b.y - a.y);
        Point ac = new Point(c.x - a.x, c.y - a.y);
        return dot(ab, ac);
    }

    static long dot(Point a, Point b) {
        long total = a.x * b.x;
        total += a.y * b.y;
        return total;
    }

    static double dist(Point a, Point b) {
        long total = (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
        return Math.sqrt(total);
    }

    static long norm(Point a) {
        long result = a.x * a.x;
        result += a.y * a.y;
        return result;
    }

    static double dist(Point a, Point b, Point x, boolean isSegment) {
        double dist = cross(a, b, x) / dist(a, b);
        // System.out.println("DIST " + dist);

        if (isSegment) {
            Point ab = new Point(b.x - a.x, b.y - a.y);

            long dot1 = dot(a, b, x);
            long norm = norm(ab);
            double u = (double) dot1 / norm;
            if (u < 0) {
                return dist(a, x);
            }

            if (u > 1) {
                return dist(b, x);
            }
        }
        return Math.abs(dist);




    }

    static long squareDist(Point a, Point b) {
        long x = a.x - b.x;
        long y = a.y - b.y;
        return x * x + y * y;
    }

    static class Point {

        int x, y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public String toString() {
            return "Point{" + "x=" + x + ", y=" + y + '}';
        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            //System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //br = new BufferedReader(new FileReader(new File("A-large (2).in")));
        }

        public String next() {


            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}