CF1269B.Modulo Equality

You are given a positive integer $m$ and two integer sequence: $a=[a_1, a_2, \ldots, a_n]$ and $b=[b_1, b_2, \ldots, b_n]$. Both of these sequence have a length $n$.

Permutation is a sequence of $n$ different positive integers from $1$ to $n$. For example, these sequences are permutations: $[1]$, $[1,2]$, $[2,1]$, $[6,7,3,4,1,2,5]$. These are not: $[0]$, $[1,1]$, $[2,3]$.

You need to find the non-negative integer $x$, and increase all elements of $a_i$ by $x$, modulo $m$ (i.e. you want to change $a_i$ to $(a_i + x) \bmod m$), so it would be possible to rearrange elements of $a$ to make it equal $b$, among them you need to find the smallest possible $x$.

In other words, you need to find the smallest non-negative integer $x$, for which it is possible to find some permutation $p=[p_1, p_2, \ldots, p_n]$, such that for all $1 \leq i \leq n$, $(a_i + x) \bmod m = b_{p_i}$, where $y \bmod m$ — remainder of division of $y$ by $m$.

For example, if $m=3$, $a = [0, 0, 2, 1], b = [2, 0, 1, 1]$, you can choose $x=1$, and $a$ will be equal to $[1, 1, 0, 2]$ and you can rearrange it to make it equal $[2, 0, 1, 1]$, which is equal to $b$.

给你一个正整数 $m$ 和两个整数序列：$a=[a_1, a_2, \ldots, a_n]$ 与 $b=[b_1, b_2, \ldots, b_n]$。这两个序列的长度均为 $n$。

排列 是由 $1$ 到 $n$ 的 $n$ 个互不相同的正整数组成的序列。例如，以下序列是排列：$[1]$、$[1,2]$、$[2,1]$、$[6,7,3,4,1,2,5]$；而以下序列不是排列：$[0]$、$[1,1]$、$[2,3]$。

你需要找出一个非负整数 $x$，使得将 $a$ 中每个元素 $a_i$ 增加 $x$ 后对 $m$ 取模（即把 $a_i$ 变为 $(a_i + x) \bmod m$），所得的新序列可以通过重新排列其元素而与 $b$ 完全相等。在所有满足条件的 $x$ 中，你需要找出最小的那个。

换言之，你需要找出最小的非负整数 $x$，使得存在某个排列 $p=[p_1, p_2, \ldots, p_n]$，满足对所有 $1 \leq i \leq n$，均有 $(a_i + x) \bmod m = b_{p_i}$，其中 $y \bmod m$ 表示 $y$ 除以 $m$ 所得的余数。

例如，若 $m=3$，$a = [0, 0, 2, 1]$，$b = [2, 0, 1, 1]$，你可以选择 $x=1$，此时 $a$ 变为 $[1, 1, 0, 2]$，再将其重排为 $[2, 0, 1, 1]$（即 $b$），即可满足要求。

The first line contains two integers $n,m$ ($1 \leq n \leq 2000, 1 \leq m \leq 10^9$): number of elemens in arrays and $m$.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \leq a_i \lt m$).

The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ($0 \leq b_i \lt m$).

It is guaranteed that there exists some non-negative integer $x$, such that it would be possible to find some permutation $p_1, p_2, \ldots, p_n$ such that $(a_i + x) \bmod m = b_{p_i}$.

第一行包含两个整数 $n,m$（$1 \leq n \leq 2000, 1 \leq m \leq 10^9$）：数组的元素个数和 $m$。

第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$0 \leq a_i \lt m$）。

第三行包含 $n$ 个整数 $b_1, b_2, \ldots, b_n$（$0 \leq b_i \lt m$）。

保证存在某个非负整数 $x$，使得存在某个排列 $p_1, p_2, \ldots, p_n$，满足 $(a_i + x) \bmod m = b_{p_i}$。

Print one integer, the smallest non-negative integer $x$, such that it would be possible to find some permutation $p_1, p_2, \ldots, p_n$ such that $(a_i + x) \bmod m = b_{p_i}$ for all $1 \leq i \leq n$.

输出一个整数，即满足条件的最小非负整数 $x$：存在某个排列 $p_1, p_2, \ldots, p_n$，使得对所有 $1 \leq i \leq n$ 均有 $(a_i + x) \bmod m = b_{p_i}$。