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:
//package Chapter3;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class preparingForTheContest {
	static class used implements Comparable<used> {
		int val, count;

		public used(int v, int count) {
			val = v;
			this.count = count;
		}

		@Override
		public int compareTo(used u) {
			return count - u.count > 0 ? 1 : count - u.count < 0 ? -1 : val - u.val;
		}
	}

	static class SegmentTree { // 1-based DS, OOP

		int N; // the number of elements in the array as a power of 2 (i.e. after padding)
		int[] array, sTree, lazy;

		SegmentTree(int[] in) {
			array = in;
			N = in.length - 1;
			sTree = new int[N << 1]; // no. of nodes = 2*N - 1, we add one to cross out index zero
			lazy = new int[N << 1];
			build(1, 1, N);
		}

		void build(int node, int b, int e) // O(n)
		{
			if (b == e)
				sTree[node] = b;
			else {
				int mid = b + e >> 1;
				build(node << 1, b, mid);
				build(node << 1 | 1, mid + 1, e);
				int val1 = array[sTree[node << 1]];
				int val2 = array[sTree[node << 1 | 1]];
				if (val1 < val2)
					sTree[node] = sTree[node << 1];
				else
					sTree[node] = sTree[node << 1 | 1];
			}
		}

		void update_point(int node, int val) // O(log n)
		{
			array[node] = val;
			// System.out.println(node+" node");
			node += N - 1;
			while (node > 1) {
				node >>= 1;
				int val1 = array[sTree[node << 1]];
				int val2 = array[sTree[node << 1 | 1]];
				if (val1 < val2)
					sTree[node] = sTree[node << 1];
				else
					sTree[node] = sTree[node << 1 | 1];

			}
		}

		int query(int i, int j) {
			return query(1, 1, N, i, j);
		}

		int query(int node, int b, int e, int i, int j) // O(log n)
		{
			if (i > e || j < b)
				return 0;
			if (b >= i && e <= j)
				return sTree[node];
			int mid = b + e >> 1;
			int q1 = query(node << 1, b, mid, i, j);
			int q2 = query(node << 1 | 1, mid + 1, e, i, j);
			int val1 = array[q1];
			int val2 = array[q2];
			if (val1 < val2)
				return q1;
			else
				return q2;

		}

	}

	static pair[] students;
	static int[] pass;
	static pair [] bugs;
	static class pair implements Comparable<pair> {
		int ability, pass, idx;

		public pair(int a, int p, int idx) {
			ability = a;
			pass = p;
			this.idx = idx;
		}

		@Override
		public int compareTo(pair p) {
			return ability - p.ability;
		}

		public String toString() {
			return ability + " " + pass + " " + idx;
		}
	}
	static boolean possDays(int count) {
		boolean poss = true;
		pass = new int[N + 1];
		Arrays.fill(pass, (int) 1e9 + 10);
		for (int i = 1; i <= n; i++) {
			pass[i] = students[i - 1].pass;
		}

		SegmentTree sg = new SegmentTree(pass);
		ArrayList<Integer> valid = new ArrayList<Integer>();
		for (int i = 0; i < bugs.length; i++) {
			bugs[i].idx = -1;
		}
		int [] taken = new int[pass.length];
		int total = 0;
		for (int i = bugs.length - 1; i >= 0; i--) {
			// System.out.println(total+" "+valid);
			int curBug = bugs[i].ability;
			int idx = findBs(curBug);
			if (idx == -1) {
				poss = false;
				break;
			} else {
				// System.out.println(idx);
				int idx2 = sg.query(idx + 1, n);
				// if(idx2==5)
				// System.out.println("hello");
				int leastPass = pass[idx2];
				if (leastPass == (int) 1e9 + 10) {
					// i am done using all students here already
					return false;
				} else if (leastPass + total > s) {
					if (i == m - 1) {
						poss = false;
						break;
					}
					return false;
//					System.out.println("hello");
				} else {
					total += leastPass;
					pair stu = students[idx2 - 1];
					bugs[i].idx = stu.idx;
					taken[idx2]++;
					while(taken[idx2]<count&&i>=1) {
						i--;
//						System.out.println("hello"+" "+bugs[i].idx+" "+stu.idx+" "+i);
						bugs[i].idx = stu.idx;
						taken[idx2]++;
					}
					// ans[bugs[i].pass]= stu.idx;
					// valid.add(idx2);
					if(taken[idx2]==count) {
					pass[idx2] = (int) (1e9) + 10;
					sg.update_point(idx2, (int) 1e9 + 10);
					}
					}
			}
		}
//		System.out.println(Arrays.toString(taken));
		if(poss) {
//			System.out.println("hello"+" "+count);
			for (int i = 0; i < bugs.length; i++) {
				ans[bugs[i].pass] = bugs[i].idx;
			}
		}
		return poss;
	}static int m,s,n,N;
	static int ans[];
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(in.readLine());
		n = Integer.parseInt(st.nextToken());
		m = Integer.parseInt(st.nextToken());
		s = Integer.parseInt(st.nextToken());
		bugs = new pair[m];
		st = new StringTokenizer(in.readLine());
		for (int i = 0; i < bugs.length; i++) {
			bugs[i] = new pair(Integer.parseInt(st.nextToken()), i, -1);
		}
		Arrays.sort(bugs);
		st = new StringTokenizer(in.readLine());
		StringTokenizer st2 = new StringTokenizer(in.readLine());
		students = new pair[n];
		for (int i = 0; i < students.length; i++) {
			students[i] = new pair(Integer.parseInt(st.nextToken()), Integer.parseInt(st2.nextToken()), i);
		}
		Arrays.sort(students);
		 N = 1;
		while (N < n)
			N <<= 1; // padding
		// System.out.println(Arrays.toString(students));

		pass = new int[N + 1];
		Arrays.fill(pass, (int) 1e9 + 10);
		for (int i = 1; i <= n; i++) {
			pass[i] = students[i - 1].pass;
		}
		// System.out.println(Arrays.toString(pass));
		int total = 0;
		ans = new int[m];
		int idxTmp = 0;
		Arrays.fill(ans, -1);
		// System.out.println(Arrays.toString(bugs));
		// System.out.println(sg.query(1, n));
//		System.out.println(Arrays.toString(students));

		// System.out.println(valid);
		boolean poss = findAns();
		if (!poss)
			System.out.println("NO");
		else {
//			PriorityQueue<used> dq = new PriorityQueue<used>();
//			// System.out.println(Arrays.toString(bugs));
//			for (int i = bugs.length - 1; i >= 0; i--) {
//				if (bugs[i].idx != -1) {
//					dq.add(new used(bugs[i].idx, 1));
//				} else {
//					used cur = dq.remove();
//					bugs[i].idx = cur.val;
//					cur.count++;
//					dq.add(cur);
//				}
//			}
//			for (int i = 0; i < bugs.length; i++) {
//				ans[bugs[i].pass] = bugs[i].idx;
//			}
			System.out.println("YES");
			for (int i = 0; i < ans.length; i++) {
				System.out.print((1 + ans[i]) + " ");
			}
		}

	}
	static boolean findAns() {
		int low = 1;
		int high = m;
		boolean poss= false;
		while(low<=high) {
			int mid =(low+high)/2;
			if(possDays(mid)) {
				poss= true;
//				System.out.println(mid);
				high = mid-1;
			}else low =mid+1;
		}
		return poss;
	}
	static int findBs(int val) {
		int low = 0;
		int high = students.length - 1;
		int ans = -1;
		while (low <= high) {
			int mid = (low + high) / 2;
			int ability = students[mid].ability;
			// System.out.println(val+" "+ability+" "+mid+" earcharing");
			if (ability >= val) {
				ans = mid;
				high = mid - 1;
			} else
				low = mid + 1;
		}
		return ans;
	}
}