761D Dasha and Very Difficult Problem[数学][思维]

D. Dasha and Very Difficult Problem

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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.

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

题意：

已知ci = bi - ai，p是从1到n的n个数字的序列，表示c中的大小顺序。先给出n表示序列长度，l，r表示序列a，b的范围。给出a序列和p序列，求出一个可能的b序列，没有输出-1

思路：

bi = ai + ci

我们求出b序列，如果b序列在l，r的给定范围内，则符合要求，如果越界，则不符合要求。为了使用这一特性，我们要求范围最小化的b序列，即求得的b序列是满足题意的最小b序列。由于p表示ci的大小顺序。 bi又与ci成线性关系。所以要使b最小，则c最小，根据题意，c序列最小即等于p序列。

所以bi = ai + pi

求得b序列中的最大值和最小值来确定b的范围，与l，r确定的范围比较即可

代码：

#include<iostream>
#include<iostream>
using namespace std;
int n, l, r;
int a[100005];
int b[100005];
int p[100005];
int main()
{
    cin >> n >> l >> r;
    for(int i = 0; i < n; ++i)
        cin >> a[i];
    for(int i = 0; i < n; ++i)
        cin >> p[i];

    int ma = - 1e9+5, mi = 1e9+5;
    for(int i = 0; i < n; ++i)
    {
        b[i] = a[i] + p[i];
        ma = max(ma, b[i]);
        mi = min(mi, b[i]);
    }

    if(ma - mi > r - l)
        cout << "-1";
    else
    {
        int temp;
        if(mi < l)
            temp = l - mi;
        else temp = r - ma;
        for(int i = 0; i < n; ++i)
            cout << b[i] + temp << " ";
    }

}