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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分