Soldier and Traveling

题面翻译

题意大概就是给定 $n$ 个城市，$m$ 条边。 然后人只能从走相邻边相连的城市。 现在给你初始城市的每一个人数，再给一组每个城市人数。询问是否可以从当前人数变换到给定人数。如果能，输入“YES”并输出方案，不能则输出“NO”。

感谢@Epiphyllum 提供的翻译

题目描述

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.

输入格式

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.

输出格式

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.

样例 #1

样例输入 #1

4 4
1 2 6 3
3 5 3 1
1 2
2 3
3 4
4 2

样例输出 #1

YES
1 0 0 0 
2 0 0 0 
0 5 1 0 
0 0 2 1

样例 #2

样例输入 #2

2 0
1 2
2 1

样例输出 #2

NO