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:
/*
If you want to aim high, aim high
Don't let that studying and grades consume you
Just live life young
******************************
What do you think? What do you think?
1st on Billboard, what do you think of it
Next is a Grammy, what do you think of it
However you think, I’m sorry, but shit, I have no fcking interest
*******************************
I'm standing on top of my Monopoly board
That means I'm on top of my game and it don't stop
til my hip don't hop anymore
https://www.a2oj.com/Ladder16.html
*******************************
300IQ as writer = Sad!
*/
import java.util.*;
import java.io.*;
import java.math.*;

   public class x1373G
   {
      static long CONS = 1696969L;
      public static void main(String hi[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int N = Integer.parseInt(st.nextToken());
         int K = Integer.parseInt(st.nextToken());
         int Q = Integer.parseInt(st.nextToken());
         //structures
         LazySegTree segtree = new LazySegTree();
         for(int v=1; v <= 400000; v++)
            segtree.update(v, v, N-v+1);
         HashSet<Long> seen = new HashSet<Long>();
         TreeMap<Integer, Integer> mset = new TreeMap<Integer, Integer>();
         StringBuilder sb = new StringBuilder();
         while(Q-->0)
         {
            st = new StringTokenizer(infile.readLine());
            int C = Integer.parseInt(st.nextToken());
            int R = Integer.parseInt(st.nextToken());
            int loc = R+Math.abs(C-K);
            long id = CONS*C+R;
            if(seen.add(id))
            {
               segtree.update(1, loc, -1);
               push(mset, loc);
            }
            else
            {
               segtree.update(1, loc, 1);
               seen.remove(id);
               pull(mset, loc);
            }
            if(mset.size() == 0)
               sb.append("0\n");
            else
            {
               int val = segtree.minQuery(1, mset.lastKey());
               if(val >= 0)   val = 0;
               sb.append(-1*val).append("\n");
            }
         }
         System.out.print(sb);
      }
      public static void push(TreeMap<Integer, Integer> map, int k)
      {
         if(!map.containsKey(k))
            map.put(k, 0);
         map.put(k, map.get(k)+1);
      }
      public static void pull(TreeMap<Integer, Integer> map, int k)
      {
         map.put(k, map.get(k)-1);
         if(map.get(k) == 0)
            map.remove(k);
      }
   }
   class LazySegTree 
   {
		private int[] min;
		private int[] lazy;
		private int size;
		public LazySegTree() 
      {
			this.size = 400000;
			min = new int[13000000];
			lazy = new int[13000000];
		}
		public void update(int l, int r, int inc) 
      {
			update(1, 0, size-1, l, r, inc);
		}
		private void pushDown(int index, int l, int r) 
      {
			min[index] += lazy[index];
			if(l != r) 
         {
				lazy[2*index] += lazy[index];
				lazy[2*index+1] += lazy[index];
			}
			lazy[index] = 0;
		}
		private void pullUp(int index, int l, int r) 
      {
			int m = (l+r)/2;
			min[index] = Math.min(evaluateMin(2*index, l, m), evaluateMin(2*index+1, m+1, r));
		}
		private int evaluateMin(int index, int l, int r) 
      {
			return min[index] + lazy[index];
		}
		private void update(int index, int l, int r, int left, int right, int inc) 
      {
			if(r < left || l > right) return;
			if(l >= left && r <= right) {
				lazy[index] += inc;
				return;
			}
			pushDown(index, l, r);
			int m = (l+r)/2;
			update(2*index, l, m, left, right, inc);
			update(2*index+1, m+1, r, left, right, inc);
			pullUp(index, l, r);
		}
		public int minQuery(int l, int r) 
      {
			return minQuery(1, 0, size-1, l, r);
		}
		private int minQuery(int index, int l, int r, int left, int right) 
      {
			if(r < left || l > right) return Integer.MAX_VALUE;
			if(l >= left && r <= right) {
				return evaluateMin(index, l, r);
			}
			pushDown(index, l, r);
			int m = (l+r)/2;
			int ret = Integer.MAX_VALUE;
			ret = Math.min(ret, minQuery(2*index, l, m, left, right));
			ret = Math.min(ret, minQuery(2*index+1, m+1, r, left, right));
			pullUp(index, l, r);
			return ret;
		}
	}