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.

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.