Soldier and Traveling

Description:

Input:

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

Next line contains n integers a₁, a₂, ..., a_n (0 ≤ a_i ≤ 100).

Next line contains n integers b₁, b₂, ..., 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.

Output:

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.

Sample Input:

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

Sample Output:

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

Sample Input:

2 0
1 2
2 1

Sample Output:

NO