Kids with Candies

You are given $n$ children, where the $i$-th child has a certain number of candies represented by an integer. Additionally, you are given an integer $E$ denoting the extra candies available. For each child, determine whether adding the extra candies to that child's current candies will allow them to have at least as many candies as any other child. Formally, if the candies of the $i$-th child is denoted as $a_i$, and $M=\max(a_1, a_2, \ldots, a_n)$, then output True for that child if and only if $a_i+E \ge M$, otherwise output False.

This problem tests your ability to manipulate arrays and perform basic comparisons. Make sure your solution reads from stdin and writes the answer to stdout.

inputFormat

The first line of input contains two integers $n$ and $E$ separated by space, where $n$ is the number of children and $E$ is the number of extra candies available. The second line contains $n$ space-separated integers $a_1, a_2, \ldots, a_n$, where $a_i$ represents the number of candies the $i$-th child has.

outputFormat

Output a single line containing $n$ boolean values (either True or False) separated by a space. The $i$-th boolean value should be True if after adding the extra candies the $i$-th child can have a candy count not less than any other child; otherwise, False.## sample

5 3
2 3 5 1 3

True True True False True