CF761D.Dasha and Very Difficult 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: c__i = b__i - a__i.

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 ≤ a__i ≤ r and l ≤ b__i ≤ r. About sequence c we know that all its elements are distinct.

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 p__i equals to the number of integers which are less than or equal to c__i 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.

达莎登录系统后开始解题。其中一题如下：

给定两个长度均为 $n$ 的序列 $a$ 和 $b$，你需要构造一个长度为 $n$ 的序列 $c$，其第 $i$ 个元素按如下方式计算：$c_i = b_i - a_i$。

关于序列 $a$ 和 $b$，已知它们的所有元素均在区间 $[l, r]$ 内。更准确地说，所有元素满足如下条件：$l \leq a_i \leq r$ 且 $l \leq b_i \leq r$。关于序列 $c$，已知其所有元素互不相同。

达莎很快写出了该题的解法，但在标准测试用例上验证她的解答却并不容易。由于评测系统存在一个错误，该测试用例中仅提供了序列 $a$ 和序列 $c$ 的压缩序列。

下面我们定义“压缩序列”：对于长度为 $n$ 的序列 $c$，其压缩序列为长度为 $n$ 的序列 $p$，其中 $p_i$ 表示序列 $c$ 中小于等于 $c_i$ 的整数的个数。例如，对序列 $c = [250,\ 200,\ 300,\ 100,\ 50]$，其压缩序列为 $p = [4,\ 3,\ 5,\ 2,\ 1]$。注意，由于 $c$ 中所有整数互不相同，因此压缩序列 $p$ 恰好包含从 $1$ 到 $n$ 的所有整数（每个恰好出现一次）。

请帮助达莎找出任意一个满足条件的序列 $b$，使得由此计算出的序列 $c$ 的压缩序列与给定的压缩序列一致。

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 _a_1,  _a_2,  ...,  a__n (l ≤ a__i ≤ r) — the elements of the sequence a.

The next line contains n distinct integers _p_1,  _p_2,  ...,  p__n (1 ≤ p__i ≤ n) — the compressed sequence of the sequence c.

第一行包含三个整数 $n$、$l$、$r$（$1 ≤ n ≤ 10^5$，$1 ≤ l ≤ r ≤ 10^9$）—— 分别表示序列的长度，以及序列 $a$ 和 $b$ 的元素取值范围 $[l, r]$。

下一行包含 $n$ 个整数 $a_1,\, a_2,\, \dots,\, a_n$（$l ≤ a_i ≤ r$）—— 序列 $a$ 的元素。

再下一行包含 $n$ 个互不相同的整数 $p_1,\, p_2,\, \dots,\, p_n$（$1 ≤ p_i ≤ n$）—— 序列 $c$ 的压缩表示。

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.

如果不存在合适的序列 $b$，则在唯一一行中输出 -1。

否则，在唯一一行中输出 $n$ 个整数——任意一个合适序列 $b$ 的元素。

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 c__i = b__i - a__i) has compressed sequence equals to p = [3, 2, 1, 4].

第二个样例中找到的序列 $b$ 是合适的，因为计算得到的序列 $c = [2 - 3,\ 2 - 4,\ 2 - 8,\ 9 - 9] = [-1,\ -2,\ -6,\ 0]$（注意 $c_i = b_i - a_i$）的压缩序列等于 $p = [3,\ 2,\ 1,\ 4]$。