Problem Statement

Given is a simple undirected graph with $N$ vertices and $M$ edges. The $i$-th edge connects Vertex ci​ and Vertex di​. Initially, Vertex $i$ has the value ai​ written on it. You want to change the values on Vertex $1$, $\dots$, Vertex $N$ to b1​, $\cdots$, bN​, 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 ax​ by $1$, and increase the value ay​ by $1$.
  • Increase the value ax​ by $1$, and decrease the value ay​ by $1$.

Determine whether it is possible to achieve the objective by properly doing the operation.

Constraints

• 1≤N≤2×105
• 0≤M≤2×105
• −109≤ai​,bi​≤109
• 1≤ci​,di​≤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 a1​ by $1$ and decrease a2​ by $1$.
• In the second operation, choose the edge connecting Vertex $2$ and $3$. Then, increase a2​ by $1$ and decrease a3​ by $1$.

This sequence of operations makes a1​=2, a2​=2, and a3​=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