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.