#745 Common Ground

Statement

Statement language

Woohyun has $N$ positive integers. Let $A_i$ denote the $i$ -th integer.

To investigate the relationships between these integers, Woohyun constructs an undirected graph with $N$ vertices. Vertex $i$ corresponds to the integer $A_i$ .

For two distinct vertices $i$ and $j$ , an edge connects them if and only if $\gcd(A_i, A_j) > 1$ .

You are given $Q$ queries. For each query, determine whether it is possible to reach vertex $v$ from vertex $u$ by following edges of the graph. If $u = v$ , the destination is considered reachable without traversing any edge.

Input

The input is given in the following format:

$N\ Q$ $A_1\ A_2\ \cdots\ A_N$

Output

For each query, print YES if the destination is reachable, or NO otherwise, on a separate line.

Constraints

$1 \leq N \leq 10^6$ .
$1 \leq Q \leq 10^6$ .

Subtasks

#	Score	Constraints
1	100	No additional constraints.

Samples

Sample 1

Input

Output

YES
NO
YES
NO
YES
NO

Vertices $1$ and $4$ are directly connected. Vertices $3$ and $5$ have no edges to other vertices. A query from a vertex to itself always has answer YES.

Sample 2

Input

Output

YES
NO
YES
YES
YES

Vertex $2$ is reachable from vertex through vertex . Vertex has no edges to other vertices.