Hackerland is a one-dimensional city with houses aligned at integral locations along a road. The Mayor wants to install radio transmitters on the roofs of the city's houses. Each transmitter has a fixed range meaning it can transmit a signal to all houses within that number of units distance away.

Given a map of Hackerland and the transmission range, determine the minimum number of transmitters so that every house is within range of at least one transmitter. Each transmitter *must* be installed on top of an existing house.

**Example**

antennae at houses and and provide complete coverage. There is no house at location to cover both and . Ranges of coverage, are , , and .

**Function Description**

Complete the *hackerlandRadioTransmitters* function in the editor below.

hackerlandRadioTransmitters has the following parameter(s):

*int x[n]:*the locations of houses*int k:*the effective range of a transmitter

**Returns**

*int:*the minimum number of transmitters to install

**Input Format**

The first line contains two space-separated integers and , the number of houses in Hackerland and the range of each transmitter.

The second line contains space-separated integers describing the respective locations of each house .

**Constraints**

- There may be more than one house at the same location.

**Subtasks**

- for of the maximum score.

**Output Format**

Print a single integer denoting the minimum number of transmitters needed to cover all of the houses.

**Sample Input 0**

STDIN Function ----- -------- 5 1 x[] size n = 5, k = 1 1 2 3 4 5 x = [1, 2, 3, 4, 5]

**Sample Output 0**

```
2
```

**Explanation 0**

The diagram below depicts our map of Hackerland:

We can cover the entire city by installing transmitters on houses at locations and .

**Sample Input 1**

```
8 2
7 2 4 6 5 9 12 11
```

**Sample Output 1**

```
3
```

**Explanation 1**

The diagram below depicts our map of Hackerland:

We can cover the entire city by installing transmitters on houses at locations , , and .