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