Problem: Dasha logged into the system and began to solve problems. One of them is as follows:

Given two sequences a and b of length n each you need to write a sequence c of length n, the i-th element of which is calculated as follows: ci = bi - ai.

About sequences a and b we know that their elements are in the range from l to r. More formally, elements satisfy the following conditions: l ≤ ai ≤ r and l ≤ bi ≤ r. About sequence c we know that all its elements are distinct.

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Dasha wrote a solution to that problem quickly, but checking her work on the standard test was not so easy. Due to an error in the test system only the sequence a and the compressed sequence of the sequence c were known from that test.

Let's give the definition to a compressed sequence. A compressed sequence of sequence c of length n is a sequence p of length n, so that pi equals to the number of integers which are less than or equal to ci in the sequence c. For example, for the sequence c = [250, 200, 300, 100, 50] the compressed sequence will be p = [4, 3, 5, 2, 1]. Pay attention that in c all integers are distinct. Consequently, the compressed sequence contains all integers from 1 to n inclusively.

Help Dasha to find any sequence b for which the calculated compressed sequence of sequence c is correct.

Input

The first line contains three integers n, l, r (1 ≤ n ≤ 105, 1 ≤ l ≤ r ≤ 109) — the length of the sequence and boundaries of the segment where the elements of sequences a and b are.

The next line contains n integers a1, a2, ..., an (l ≤ ai ≤ r) — the elements of the sequence a.

The next line contains n distinct integers p1, p2, ..., pn (1 ≤ pi ≤ n) — the compressed sequence of the sequence c.

Output

If there is no the suitable sequence b, then in the only line print "-1".

Otherwise, in the only line print n integers — the elements of any suitable sequence b.

Examples

Input

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


Output

3 1 5 4 2 

Input

4 2 9
3 4 8 9
3 2 1 4


Output

2 2 2 9 

Input

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


Output

-1

Note

Sequence b which was found in the second sample is suitable, because calculated sequence c = [2 - 3, 2 - 4, 2 - 8, 9 - 9] = [ - 1, - 2, - 6, 0] (note that ci = bi - ai) has compressed sequence equals to p = [3, 2, 1, 4].

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.Scanner;

public class D {

	class X {
		int k, p;
		long a, b, c;

		X(int k, long a) {
			this.k = k;
			this.a = a;
		}
	}

	private void work() {
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));

		int n = sc.nextInt();
		long L = sc.nextInt();
		long R = sc.nextInt();

		List<X> list = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			list.add(new X(i, sc.nextInt()));
		}
		for (int i = 0; i < n; i++) {
			list.get(i).p = sc.nextInt();
		}

		Collections.sort(list, new Comparator<X>() {
			@Override
			public int compare(X o1, X o2) {
				return o1.p - o2.p;
			}
		});

		list.get(0).b = L;
		list.get(0).c = L - list.get(0).a;

		for (int i = 1; i < n; i++) {
			long nextC = list.get(i - 1).c + 1;
			long nextB = nextC + list.get(i).a;
			if (nextB < L)
				nextB = L;
			if (nextB > R) {
				list = null;
				break;
			}
			list.get(i).b = nextB;
			list.get(i).c = nextB - list.get(i).a;
		}

		if (list == null) {
			System.out.println("-1");
		} else {
			Collections.sort(list, new Comparator<X>() {
				@Override
				public int compare(X o1, X o2) {
					return o1.k - o2.k;
				}
			});
			for (int i = 0; i < n; i++) {
				if (i > 0)
					System.out.print(" ");
				System.out.print(list.get(i).b);
			}
			System.out.println();
		}

		sc.close();
	}

	public static void main(String[] args) {
		new D().work();
	}

}