Problem:
Max Score: 500 Points

Problem Statement

We have a grid with n rows and 7 columns. We call it a calendar. The cell at i-th row and j-th column is denoted (i, j).

Initially, each cell at (i, j) contains the integer 7i + j - 8, and each cell is white.

Snuke likes painting, so he decided integer m, and did q operations with a calendar.

・In i-th operation, he paint black on the cell in which an integer is written such remainder of dividing by m is a_i.

Please count the number of connected white parts.

Note that if two adjacent cells are white, the cells belong to the same connected part.

Input Format

The input format is following:

n m q
a_1 a_2 ... a_q

Output Format

Print the number of connected part in one line.

Constraints

n ≤ 10^{12}

7n is divisible by m.

1 ≤ q ≤ m ≤ 10^5

0 ≤ a_1 < a_2 < ... < a_q < m

Scoring

Subtask 1 [100 points]

n ≤ 100000.

Subtask 2 [90 points]

m is divisible by 7.

a_{i + 1} - a_i = 1.

Subtask 3 [200 points]

m is divisible by 7.

Subtask 4 [110 points]

There are no additional constraints.

Sample Input 1

7 7 3
1 3 5

Sample Output 1

4

The calendar looks like this:

Sample Input 2

10 14 8
5 6 7 8 9 10 11 12

Sample Output 2

10

The calendar looks like this:

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static void solve()
	{
		long n = nl();
		int m = ni();
		int q = ni();
		int[] a = na(q);
		if(m % 7 != 0){
			a = Arrays.copyOf(a, q*7);
			for(int i = q;i < q*7;i++){
				a[i] = a[i-q] + m;
			}
			m *= 7;
			q *= 7;
		}
		tr(m);
		boolean[] map = new boolean[m];
		Arrays.fill(map, true);
		for(int v : a)map[v] = false;
		int c1 = count(map);
		
		map = new boolean[2*m];
		Arrays.fill(map, true);
		for(int v : a)map[v] = map[v+m] = false;
		int c2 = count(map);
		out.println(c1 + (c2-c1) * (7*n/m-1));
	}
	
	static int count(boolean[] map){
		int m = map.length;
		DJSet ds = new DJSet(m);
		for(int i = 0;i < m/7;i++){
			for(int j = 0;j < 7;j++){
				if(j+1 < 7 && map[i*7+j] && map[i*7+j+1]){
					ds.union(i*7+j, i*7+j+1);
				}
				if(i+1 < m/7 && map[i*7+j] && map[(i+1)*7+j]){
					ds.union(i*7+j, (i+1)*7+j);
				}
			}
		}
		int ct = 0;
		for(int i = 0;i < m;i++){
			if(ds.upper[i] < 0 && map[i]){
				ct++;
			}
		}
		return ct;
	}
	
	public static class DJSet {
		public int[] upper;

		public DJSet(int n) {
			upper = new int[n];
			Arrays.fill(upper, -1);
		}

		public int root(int x) {
			return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
		}

		public boolean equiv(int x, int y) {
			return root(x) == root(y);
		}

		public boolean union(int x, int y) {
			x = root(x);
			y = root(y);
			if (x != y) {
				if (upper[y] < upper[x]) {
					int d = x;
					x = y;
					y = d;
				}
				upper[x] += upper[y];
				upper[y] = x;
			}
			return x == y;
		}

		public int count() {
			int ct = 0;
			for (int u : upper)
				if (u < 0)
					ct++;
			return ct;
		}
	}

	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private static char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}