Problem Statement

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.

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.

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.

Sample Input 1

3 2
1 2 3
2 2 2
1 2
2 3

Sample Output 1

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.

Sample Input 2

1 0
5
5

Sample Output 2

Yes

The objective may be achieved already in the beginning.

Sample Input 3

2 1
1 1
2 1
1 2

Sample Output 3

No

There is no way to do the operation to achieve the objective.

Sample Input 4

17 9
-905371741 -999219903 969314057 -989982132 -87720225 -175700172 -993990465 929461728 895449935 -999016241 782467448 -906404298 578539175 9684413 -619191091 -952046546 125053320
-440503430 -997661446 -912471383 -995879434 932992245 -928388880 -616761933 929461728 210953513 -994677396 648190629 -530944122 578539175 9684413 595786809 -952046546 125053320
2 10
6 12
9 11
11 5
7 6
3 15
3 1
1 9
10 4

Sample Output 4

Yes

见题面 Input 部分

见题面 Output 部分