Micro-World

2000ms

262144K

Description:

You have a Petri dish with bacteria and you are preparing to dive into the harsh micro-world. But, unfortunately, you don't have any microscope nearby, so you can't watch them.

You know that you have $$$n$$$ bacteria in the Petri dish and size of the $$$i$$$-th bacteria is $$$a_i$$$. Also you know intergalactic positive integer constant $$$K$$$.

The $$$i$$$-th bacteria can swallow the $$$j$$$-th bacteria if and only if $$$a_i > a_j$$$ and $$$a_i \le a_j + K$$$. The $$$j$$$-th bacteria disappear, but the $$$i$$$-th bacteria doesn't change its size. The bacteria can perform multiple swallows. On each swallow operation any bacteria $$$i$$$ can swallow any bacteria $$$j$$$ if $$$a_i > a_j$$$ and $$$a_i \le a_j + K$$$. The swallow operations go one after another.

For example, the sequence of bacteria sizes $$$a=[101, 53, 42, 102, 101, 55, 54]$$$ and $$$K=1$$$. The one of possible sequences of swallows is: $$$[101, 53, 42, 102, \underline{101}, 55, 54]$$$ $$$\to$$$ $$$[101, \underline{53}, 42, 102, 55, 54]$$$ $$$\to$$$ $$$[\underline{101}, 42, 102, 55, 54]$$$ $$$\to$$$ $$$[42, 102, 55, \underline{54}]$$$ $$$\to$$$ $$$[42, 102, 55]$$$. In total there are $$$3$$$ bacteria remained in the Petri dish.

Since you don't have a microscope, you can only guess, what the minimal possible number of bacteria can remain in your Petri dish when you finally will find any microscope.

Input:

The first line contains two space separated positive integers $$$n$$$ and $$$K$$$ ($$$1 \le n \le 2 \cdot 10^5$$$, $$$1 \le K \le 10^6$$$) — number of bacteria and intergalactic constant $$$K$$$.

The second line contains $$$n$$$ space separated integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^6$$$) — sizes of bacteria you have.

Output:

Print the only integer — minimal possible number of bacteria can remain.

Sample Input:

7 1
101 53 42 102 101 55 54

Sample Output:

Sample Input:

6 5
20 15 10 15 20 25

Sample Output:

Sample Input:

7 1000000
1 1 1 1 1 1 1

Sample Output:

Note:

The first example is clarified in the problem statement.

In the second example an optimal possible sequence of swallows is: $$$[20, 15, 10, 15, \underline{20}, 25]$$$ $$$\to$$$ $$$[20, 15, 10, \underline{15}, 25]$$$ $$$\to$$$ $$$[20, 15, \underline{10}, 25]$$$ $$$\to$$$ $$$[20, \underline{15}, 25]$$$ $$$\to$$$ $$$[\underline{20}, 25]$$$ $$$\to$$$ $$$[25]$$$.

In the third example no bacteria can swallow any other bacteria.

Informação

Provedor Codeforces

Código CF990B