Given is a simple undirected graph with N vertices and M edges. The i-th edge connects Vertex c_i and Vertex d_i.
Initially, Vertex i has the value a_i written on it. You want to change the values on Vertex $1, \ldots, Vertex N$ to $b_1, \cdots, b_N,$ respectively, by doing the operation below zero or more times.
- Choose an edge, and let Vertex x and Vertex y be the vertices connected by that edge. Choose one of the following and do it:
- Decrease the value a_x by 1, and increase the value a_y by 1.
- Increase the value a_x by 1, and decrease the value a_y by 1.
Determine whether it is possible to achieve the objective by properly doing the operation.

-----Constraints-----
- $1 \leq N \leq 2 \times 10^5$
- $0 \leq M \leq 2 \times 10^5$
- -$10^9 \leq a_i,b_i \leq 10^9$
- $1 \leq c_i,d_i \leq N$
- The given graph is simple, that is, has no self-loops and no multi-edges.
- All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N M
$a_1 \cdots a_N$
$b_1 \cdots b_N$
c_1 d_1
$\vdots$
c_M d_M

-----Output-----
Print Yes if it is possible to achieve the objective by properly doing the operation, and No otherwise.

-----Sample Input-----
3 2
1 2 3
2 2 2
1 2
2 3

-----Sample Output-----
Yes

You can achieve the objective by, for example, doing the operation as follows:
- In the first operation, choose the edge connecting Vertex 1 and 2. Then, increase a_1 by 1 and decrease a_2 by 1.
- In the second operation, choose the edge connecting Vertex 2 and 3. Then, increase a_2 by 1 and decrease a_3 by 1.
This sequence of operations makes a_1=2, a_2=2, and a_3=2.

见题面

见题面