CF1615H.Reindeer Games

There are $n$ reindeer at the North Pole, all battling for the highest spot on the "Top Reindeer" leaderboard on the front page of CodeNorses (a popular competitive reindeer gaming website). Interestingly, the "Top Reindeer" title is just a measure of upvotes and has nothing to do with their skill level in the reindeer games, but they still give it the utmost importance.

Currently, the $i$-th reindeer has a score of $a_i$. You would like to influence the leaderboard with some operations. In an operation, you can choose a reindeer, and either increase or decrease his score by $1$ unit. Negative scores are allowed.

You have $m$ requirements for the resulting scores. Each requirement is given by an ordered pair $(u, v)$, meaning that after all operations, the score of reindeer $u$ must be less than or equal to the score of reindeer $v$.

Your task is to perform the minimum number of operations so that all requirements will be satisfied.

在北极有 $n$ 只驯鹿，它们都在争夺 CodeNorses（一个广受欢迎的驯鹿竞技游戏网站）首页“顶尖驯鹿”排行榜上的最高排名。有趣的是，“顶尖驯鹿”头衔仅由点赞数决定，与其在驯鹿游戏中的实际技能水平毫无关系，但它们依然对此极为重视。

目前，第 $i$ 只驯鹿的得分为 $a_i$。你希望通过若干操作来影响该排行榜。每次操作中，你可以任选一只驯鹿，并将其得分增加或减少 $1$ 单位。允许出现负分。

你对最终得分有 $m$ 项约束条件。每项约束由一个有序对 $(u, v)$ 给出，表示在所有操作完成后，驯鹿 $u$ 的得分必须小于等于驯鹿 $v$ 的得分。

你的任务是执行最少次数的操作，使得所有约束条件均被满足。

The first line contains two integers $n$ and $m$ ($2\le n\le 1000$; $1\le m\le 1000$) — the number of reindeer and requirements, respectively.

The second line contains $n$ integers $a_1,\ldots, a_n$ ($1\le a_i\le 10^9$), where $a_i$ is the current score of reindeer $i$.

The next $m$ lines describe the requirements.

The $i$-th of these lines contains two integers $u_i$ and $v_i$ ($1\le u_i, v_i\le n$; $u_i\ne v_i$) — the two reindeer of the $i$-th requirement.

第一行包含两个整数 $n$ 和 $m$（$2\le n\le 1000$；$1\le m\le 1000$），分别表示驯鹿的数量和要求的数量。

第二行包含 $n$ 个整数 $a_1,\ldots, a_n$（$1\le a_i\le 10^9$），其中 $a_i$ 表示第 $i$ 只驯鹿当前的得分。

接下来的 $m$ 行描述各项要求。

其中第 $i$ 行包含两个整数 $u_i$ 和 $v_i$（$1\le u_i, v_i\le n$；$u_i\ne v_i$），表示第 $i$ 项要求所涉及的两只驯鹿。

Print $n$ integers $b_1,\ldots, b_n$ ($-10^{15}\le b_i\le 10^{15}$), where $b_i$ is the score of the $i$-th reindeer after all operations.

If there are multiple solutions achieving the minimum number of operations, you may output any.

We can prove that there is always an optimal solution such that $|b_i|\le 10^{15}$ for all $i$.

输出 $n$ 个整数 $b_1,\ldots, b_n$（满足 $-10^{15}\le b_i\le 10^{15}$），其中 $b_i$ 表示第 $i$ 只驯鹿在所有操作完成后的得分。

若存在多种方案均能达到最少操作次数，你可以输出其中任意一种。

我们可以证明：总存在一种最优解，使得对所有 $i$ 均有 $|b_i|\le 10^{15}$。