Pencils and Boxes

给出$n$个整数$a_1,a_2,...,a_n$，现在需要对其进行分组，使其满足以下条件： - 每个数都必须恰好分入一组中 - 每一组中必须至少包含$k$个数 - 在每一组中，整数的权值之差的绝对值不能超过$d$。即当$a_i,a_j$在同一组时，需要满足$|a_i-a_j| \leq d$ 请判断是否存在满足条件的分组方案，若有请输出"YES",否则输出"NO"。 数据范围：$1\leq k \leq n \leq 5 * 10^5 , 0 \leq d \leq 10^9$

Mishka received a gift of multicolored pencils for his birthday! Unfortunately he lives in a monochrome world, where everything is of the same color and only saturation differs. This pack can be represented as a sequence $ a_{1},a_{2},...,a_{n} $ of $ n $ integer numbers — saturation of the color of each pencil. Now Mishka wants to put all the mess in the pack in order. He has an infinite number of empty boxes to do this. He would like to fill some boxes in such a way that: - Each pencil belongs to exactly one box; - Each non-empty box has at least $ k $ pencils in it; - If pencils $ i $ and $ j $ belong to the same box, then $ |a_{i}-a_{j}|<=d $ , where $ |x| $ means absolute value of $ x $ . Note that the opposite is optional, there can be pencils $ i $ and $ j $ such that $ |a_{i}-a_{j}|<=d $ and they belong to different boxes. Help Mishka to determine if it's possible to distribute all the pencils into boxes. Print "YES" if there exists such a distribution. Otherwise print "NO".

The first line contains three integer numbers $ n $ , $ k $ and $ d $ ( $ 1<=k<=n<=5·10^{5} $ , $ 0<=d<=10^{9} $ ) — the number of pencils, minimal size of any non-empty box and maximal difference in saturation between any pair of pencils in the same box, respectively. The second line contains $ n $ integer numbers $ a_{1},a_{2},...,a_{n} $ ( $ 1<=a_{i}<=10^{9} $ ) — saturation of color of each pencil.

Print "YES" if it's possible to distribute all the pencils into boxes and satisfy all the conditions. Otherwise print "NO".

6 3 10
7 2 7 7 4 2

YES

6 2 3
4 5 3 13 4 10

YES

3 2 5
10 16 22

NO

In the first example it is possible to distribute pencils into $ 2 $ boxes with $ 3 $ pencils in each with any distribution. And you also can put all the pencils into the same box, difference of any pair in it won't exceed $ 10 $ . In the second example you can split pencils of saturations $ [4,5,3,4] $ into $ 2 $ boxes of size $ 2 $ and put the remaining ones into another box.