CF546E.Soldier and Traveling

In the country there are n cities and m bidirectional roads between them. Each city has an army. Army of the i-th city consists of a__i soldiers. Now soldiers roam. After roaming each soldier has to either stay in his city or to go to the one of neighboring cities by at moving along at most one road.

Check if is it possible that after roaming there will be exactly b__i soldiers in the i-th city.

该国共有 $n$ 座城市，以及它们之间连接的 $m$ 条双向道路。每座城市都拥有一支军队，其中第 $i$ 座城市的军队由 $a_i$ 名士兵组成。现在士兵们开始移动。移动结束后，每名士兵必须要么留在自己原来的城市，要么沿至多一条道路前往一个相邻城市。

请判断：移动结束后，是否可能使得第 $i$ 座城市中恰好有 $b_i$ 名士兵？

First line of input consists of two integers n and m (1 ≤ n ≤ 100, 0 ≤ m ≤ 200).

Next line contains n integers _a_1, _a_2, ..., a__n (0 ≤ a__i ≤ 100).

Next line contains n integers _b_1, _b_2, ..., b__n (0 ≤ b__i ≤ 100).

Then m lines follow, each of them consists of two integers p and q (1 ≤ p, q ≤ n, p ≠ q) denoting that there is an undirected road between cities p and q.

It is guaranteed that there is at most one road between each pair of cities.

输入的第一行包含两个整数 $n$ 和 $m$（$1 \leq n \leq 100$，$0 \leq m \leq 200$）。

第二行包含 $n$ 个整数 $a_1,\,a_2,\,\dots,\,a_n$（$0 \leq a_i \leq 100$）。

第三行包含 $n$ 个整数 $b_1,\,b_2,\,\dots,\,b_n$（$0 \leq b_i \leq 100$）。

接下来是 $m$ 行，每行包含两个整数 $p$ 和 $q$（$1 \leq p,\,q \leq n$，$p \neq q$），表示城市 $p$ 与城市 $q$ 之间存在一条无向道路。

保证任意两个城市之间至多只有一条道路。

If the conditions can not be met output single word "NO".

Otherwise output word "YES" and then n lines, each of them consisting of n integers. Number in the i-th line in the j-th column should denote how many soldiers should road from city i to city j (if i ≠ j) or how many soldiers should stay in city i (if i = j).

If there are several possible answers you may output any of them.

如果无法满足条件，则输出单个单词 “NO”。

否则，输出单词 “YES”，然后输出 $n$ 行，每行包含 $n$ 个整数。第 $i$ 行第 $j$ 列的数字应表示从城市 $i$ 前往城市 $j$ 的士兵人数（若 $i \neq j$），或留在城市 $i$ 的士兵人数（若 $i = j$）。

若存在多种可能的答案，输出任意一种即可。