A10862 | 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.

The first line contains three integers $n$ , $l$ , $r$ $(1<=n<=10^{5},1<=l<=r<=10^{9})$ — 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 $c$ .

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 $b$ .