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.

Input

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 $*c*$.

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 $*b*$.

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 $*c*_{*i*} = *b*_{*i*} - *a*_{*i*}$) has compressed sequence equals to $*p* = [3, 2, 1, 4]$.