Problem:
Score : 300 points

Problem Statement

Every day, N passengers arrive at Takahashi Airport.
The i-th passenger arrives at time T_i.

Every passenger arrived at Takahashi airport travels to the city by bus. Each bus can accommodate up to C passengers.
Naturally, a passenger cannot take a bus that departs earlier than the airplane arrives at the airport.
Also, a passenger will get angry if he/she is still unable to take a bus K units of time after the arrival of the airplane.
For that reason, it is necessary to arrange buses so that the i-th passenger can take a bus departing at time between T_i and T_i + K (inclusive).

When setting the departure times for buses under this condition, find the minimum required number of buses.
Here, the departure time for each bus does not need to be an integer, and there may be multiple buses that depart at the same time.

Constraints

2 \leq N \leq 100000

1 \leq C \leq 10^9

1 \leq K \leq 10^9

1 \leq T_i \leq 10^9

C, K and T_i are integers.

Input

The input is given from Standard Input in the following format:

N C K
T_1
T_2
:
T_N

Output

Print the minimum required number of buses.

Sample Input 1

5 3 5
1
2
3
6
12

Sample Output 1

3

For example, the following three buses are enough:

A bus departing at time 4.5, that carries the passengers arriving at time 2 and 3.

A bus departing at time 6, that carries the passengers arriving at time 1 and 6.

A bus departing at time 12, that carries the passenger arriving at time 12.

Sample Input 2

6 3 3
7
6
2
8
10
6

Sample Output 2

3

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)


import java.text.DecimalFormat;
import java.util.stream.LongStream;
import java.util.stream.IntStream;
import java.io.*;
import java.util.*;

public class Main {

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);

        AtCoder problem = new AtCoder(sc);
        problem.solve(sc, out);

        out.flush();
    }

}

class AtCoder {

    int N, C, K;
    int[] T;

    AtCoder(FastScanner sc) {
        N = sc.nextInt();
        C = sc.nextInt();
        K = sc.nextInt();
        T = sc.arrayInt(N);
    }

    void solve(FastScanner sc, PrintWriter out) {
        Arrays.sort(T);
        out.println(Arrays.toString(T));
        int ans = 0;
        int u = T[0] + K;
        int limit = C - 1;
        for (int i = 1; i < N; i++) {
            int t = T[i];
            if (t <= u && limit > 0) {
                limit--;
            } else {
                ans++;
                u = t + K;
                limit = C - 1;
            }
            if (i == N - 1) ans++;
        }
        out.println(ans);
    }

}

class FastScanner {

    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte()) {
            return buffer[ptr++];
        } else {
            return -1;
        }
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr])) {
            ptr++;
        }
        return hasNextByte();
    }

    public String next() {
        if (!hasNext()) {
            throw new NoSuchElementException();
        }
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext()) {
            throw new NoSuchElementException();
        }
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) {
            throw new NumberFormatException();
        }
        return (int) nl;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public int[] arrayInt(int N) {
        int[] array = new int[N];
        for (int i = 0; i < N; i++) {
            array[i] = nextInt();
        }
        return array;
    }

    public long[] arrayLong(int N) {
        long[] array = new long[N];
        for (int i = 0; i < N; i++) {
            array[i] = nextLong();
        }
        return array;
    }

    public double[] arrayDouble(int N) {
        double[] array = new double[N];
        for (int i = 0; i < N; i++) {
            array[i] = nextDouble();
        }
        return array;
    }

    public String[] arrayString(int N) {
        String[] array = new String[N];
        for (int i = 0; i < N; i++) {
            array[i] = next();
        }
        return array;
    }

    public int randomInt() {
        Random r = new Random();
        int value = r.nextInt((int) 1e6);
        System.out.println(value);
        return value;
    }

    public int[] randomInt(int N) {
        int[] array = new int[N];
        Random r = new Random();
        for (int i = 0; i < N; i++) {
            array[i] = r.nextInt((int) 1e6);
        }
        System.out.println(Arrays.toString(array));
        return array;
    }

}

class My {

    static void ans(boolean b) {
        System.out.println(b ? "Yes" : "No");
    }

    static void ANS(boolean b) {
        System.out.println(b ? "YES" : "NO");
    }

    static String sort(String s) {
        char[] ch = s.toCharArray();
        Arrays.sort(ch);
        return String.valueOf(ch);
    }

    static String reverse(String s) {
        return new StringBuilder(s).reverse().toString();
    }

    static int[] reverse(int[] array) {
        for (int i = 0; i < array.length / 2; i++) {
            int temp = array[i];
            array[i] = array[array.length - 1 - i];
            array[array.length - 1 - i] = temp;
        }
        return array;
    }

    static long[] reverse(long[] array) {
        for (int i = 0; i < array.length / 2; i++) {
            long temp = array[i];
            array[i] = array[array.length - 1 - i];
            array[array.length - 1 - i] = temp;
        }
        return array;
    }

    static double[] reverse(double[] array) {
        for (int i = 0; i < array.length / 2; i++) {
            double temp = array[i];
            array[i] = array[array.length - 1 - i];
            array[array.length - 1 - i] = temp;
        }
        return array;
    }

    static String[] reverse(String[] array) {
        for (int i = 0; i < array.length / 2; i++) {
            String temp = array[i];
            array[i] = array[array.length - 1 - i];
            array[array.length - 1 - i] = temp;
        }
        return array;
    }

    static char[] reverse(char[] array) {
        for (int i = 0; i < array.length / 2; i++) {
            char temp = array[i];
            array[i] = array[array.length - 1 - i];
            array[array.length - 1 - i] = temp;
        }
        return array;
    }

    static long min(long... numbers) {
        Arrays.sort(numbers);
        return numbers[0];
    }

    static int min(int... numbers) {
        Arrays.sort(numbers);
        return numbers[0];
    }

    static double min(double... numbers) {
        Arrays.sort(numbers);
        return numbers[0];
    }

    static long max(long... numbers) {
        Arrays.sort(numbers);
        return numbers[numbers.length - 1];
    }

    static int max(int... numbers) {
        Arrays.sort(numbers);
        return numbers[numbers.length - 1];
    }

    static double max(double... numbers) {
        Arrays.sort(numbers);
        return numbers[numbers.length - 1];
    }

    static int sum(long number) {
        int sum = 0;
        while (number > 0) {
            sum += number % 10;
            number /= 10;
        }
        return sum;
    }

}