Problem: You are given a chessboard consisting of n rows and n columns. Rows are numbered from bottom to top from 1 to n. Columns are numbered from left to right from 1 to n. The cell at the intersection of the x-th column and the y-th row is denoted as (x, y). Furthermore, the k-th column is a special column. 

Initially, the board is empty. There are m changes to the board. During the i-th change one pawn is added or removed from the board. The current board is good if we can move all pawns to the special column by the followings rules:

  * Pawn in the cell (x, y) can be moved to the cell (x, y + 1), (x - 1, y + 1) or (x + 1, y + 1); 
  * You can make as many such moves as you like; 
  * Pawns can not be moved outside the chessboard; 
  * Each cell can not contain more than one pawn. 



The current board may not always be good. To fix it, you can add new rows to the board. New rows are added at the top, i. e. they will have numbers n+1, n+2, n+3, ....

After each of m changes, print one integer — the minimum number of rows which you have to add to make the board good.

Input

The first line contains three integers n, k and m (1 ≤ n, m ≤ 2 ⋅ 10^5; 1 ≤ k ≤ n) — the size of the board, the index of the special column and the number of changes respectively.

Then m lines follow. The i-th line contains two integers x and y (1 ≤ x, y ≤ n) — the index of the column and the index of the row respectively. If there is no pawn in the cell (x, y), then you add a pawn to this cell, otherwise — you remove the pawn from this cell.

Output

After each change print one integer — the minimum number of rows which you have to add to make the board good.

Example

Input


5 3 5
4 4
3 5
2 4
3 4
3 5


Output


0
1
2
2
1

Solution (in JAVA):

Solution:
//package ecr90;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Set;

public class G {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni(), K = ni(), m = ni();
		Set<Long> pawns = new HashSet<>();
		int D = 600010;
		int[] a = new int[D];
		for(int i = 0;i < D;i++){
			a[i] = -i;
		}
		StarrySkyTree sst = new StarrySkyTree(a);
		
		for(int z = 0;z < m;z++){
			int c = ni(), r = ni()-1;
			r += Math.abs(c - K);
			long key = (long)c<<32|r;
			if(pawns.contains(key)){
				pawns.remove(key);
				sst.add(0, r+1, 1);
			}else{
				pawns.add(key);
				sst.add(0, r+1, -1);
			}
			// 0 -1 -2 -3 -4 -5
			// -1 -2 -3 -4 -4 -5
			int low = 0, high = D+1;
			while(high - low > 1){
				int h = high+low>>1;
				if(sst.min(0, h) >= -(h-1)){
					high = h;
				}else{
					low = h;
				}
			}
			out.println(Math.max(0, high-(n+1)));
		}
	}
	
	public class StarrySkyTree {
		public int M, H, N;
		public int[] st;
		public int[] plus;
		public int I = Integer.MAX_VALUE/2; // I+plus<int
		
		public StarrySkyTree(int n)
		{
			N = n;
			M = Integer.highestOneBit(Math.max(n-1, 1))<<2;
			H = M>>>1;
			st = new int[M];
			plus = new int[H];
		}
		
		public StarrySkyTree(int[] a)
		{
			N = a.length;
			M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
			H = M>>>1;
			st = new int[M];
			for(int i = 0;i < N;i++){
				st[H+i] = a[i];
			}
			plus = new int[H];
			Arrays.fill(st, H+N, M, I);
			for(int i = H-1;i >= 1;i--)propagate(i);
		}
		
		private void propagate(int i)
		{
			st[i] = Math.min(st[2*i], st[2*i+1]) + plus[i];
		}
		
		public void add(int l, int r, int v){ if(l < r)add(l, r, v, 0, H, 1); }
		
		private void add(int l, int r, int v, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				if(cur >= H){
					st[cur] += v;
				}else{
					plus[cur] += v;
					propagate(cur);
				}
			}else{
				int mid = cl+cr>>>1;
				if(cl < r && l < mid){
					add(l, r, v, cl, mid, 2*cur);
				}
				if(mid < r && l < cr){
					add(l, r, v, mid, cr, 2*cur+1);
				}
				propagate(cur);
			}
		}
		
		public int min(int l, int r){ return l >= r ? I : min(l, r, 0, H, 1);}
		
		private int min(int l, int r, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				return st[cur];
			}else{
				int mid = cl+cr>>>1;
				int ret = I;
				if(cl < r && l < mid){
					ret = Math.min(ret, min(l, r, cl, mid, 2*cur));
				}
				if(mid < r && l < cr){
					ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1));
				}
				return ret + plus[cur];
			}
		}
		
		public void fall(int i)
		{
			if(i < H){
				if(2*i < H){
					plus[2*i] += plus[i];
					plus[2*i+1] += plus[i];
				}
				st[2*i] += plus[i];
				st[2*i+1] += plus[i];
				plus[i] = 0;
			}
		}
		
		public int firstle(int l, int v) {
			if(l >= H)return -1;
			int cur = H+l;
			for(int i = 1, j = Integer.numberOfTrailingZeros(H)-1;i <= cur;j--){
				fall(i);
				i = i*2|cur>>>j&1;
			}
			while(true){
				fall(cur);
				if(st[cur] <= v){
					if(cur >= H)return cur-H;
					cur = 2*cur;
				}else{
					cur++;
					if((cur&cur-1) == 0)return -1;
					cur = cur>>>Integer.numberOfTrailingZeros(cur);
				}
			}
		}
		
		public int lastle(int l, int v) {
			if(l < 0)return -1;
			int cur = H+l;
			for(int i = 1, j = Integer.numberOfTrailingZeros(H)-1;i <= cur;j--){
				fall(i);
				i = i*2|cur>>>j&1;
			}
			while(true){
				fall(cur);
				if(st[cur] <= v){
					if(cur >= H)return cur-H;
					cur = 2*cur+1;
				}else{
					if((cur&cur-1) == 0)return -1;
					cur = cur>>>Integer.numberOfTrailingZeros(cur);
					cur--;
				}
			}
		}
		
		public int[] toArray() { return toArray(1, 0, H, new int[H]); }
		
		private int[] toArray(int cur, int l, int r, int[] ret)
		{
			if(r-l == 1){
				ret[cur-H] = st[cur];
			}else{
				toArray(2*cur, l, l+r>>>1, ret);
				toArray(2*cur+1, l+r>>>1, r, ret);
				for(int i = l;i < r;i++)ret[i] += plus[cur];
			}
			return ret;
		}
	}

	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new G().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private 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 boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private 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 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 int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private 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 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 boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}