201413: [AtCoder]ARC141 D - Non-divisible Set

Problem Statement

We say that a set $S$ of positive integers is good when, for any $a,\ b \in S\ (a\neq b)$, $b$ is not a multiple of $a$.

You are given a set of $N$ integers between $1$ and $2M$ (inclusive): $S=\lbrace A_1,\ A_2,\ \dots,\ A_N\rbrace$.

For each $i=1,\ 2,\ \dots,\ N$, determine whether there exists a good set with $M$ elements that is a subset of $S$ containing $A_i$.

Constraints

• $M \leq N \leq 2M$
• $1 \leq M \leq 3 \times 10^5$
• $1 \leq A_1 < A_2 < \dots < A_N \leq 2M$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$
$A_1$ $A_2$ $\dots$ $A_{N}$

Output

Print $N$ lines. The $i$-th line should contain Yes if there exists a good set with $M$ elements that is a subset of $S$ containing $A_i$, and No otherwise.

Sample Input 1

5 3
1 2 3 4 5

Sample Output 1

No
Yes
Yes
Yes
Yes

Trivially, the only good set containing $A_1=1$ is $\lbrace 1\rbrace$, which has just one element, so the answer for $i=1$ is No.

There is a good set $\lbrace 2,\ 3,\ 5\rbrace$ containing $A_2=2$, so the answer for $i=2$ is Yes.

Sample Input 2

4 4
2 4 6 8

Sample Output 2

No
No
No
No

Sample Input 3

13 10
2 3 4 6 7 9 10 11 13 15 17 19 20

Sample Output 3

No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No