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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
mt19937 gene(233);
inline char GET_CHAR() {
  const int maxn = 131072;
  static char buf[maxn], *p1 = buf, *p2 = buf;
  return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, maxn, stdin), p1 == p2)
             ? EOF
             : *p1++;
}
inline int getInt() {
  int res(0);
  char c = getchar();
  while (c < '0') c = getchar();
  while (c >= '0') {
    res = res * 10 + (c - '0');
    c = getchar();
  }
  return res;
}
inline long long fastpo(long long x, long long n, long long mod) {
  long long res(1);
  while (n) {
    if (n & 1) {
      res = res * (long long)x % mod;
    }
    x = x * (long long)x % mod;
    n /= 2;
  }
  return res;
}
inline string itoa(int x, int width = 0) {
  string res;
  if (x == 0) res.push_back('0');
  while (x) {
    res.push_back('0' + x % 10);
    x /= 10;
  }
  while ((int)res.size() < width) res.push_back('0');
  reverse(res.begin(), res.end());
  return res;
}
const int _B = 131072;
char buf[_B];
int _bl = 0;
inline void flush() {
  fwrite(buf, 1, _bl, stdout);
  _bl = 0;
}
__inline void _putchar(char c) {
  if (_bl == _B) flush();
  buf[_bl++] = c;
}
inline void print(long long x, char c) {
  static char tmp[20];
  int l = 0;
  if (!x)
    tmp[l++] = '0';
  else {
    while (x) {
      tmp[l++] = x % 10 + '0';
      x /= 10;
    }
  }
  for (int i = l - 1; i >= 0; i--) _putchar(tmp[i]);
  _putchar(c);
}
const int N = 400033;
const int LOG = 20;
const int mod = 1e9 + 7;
const int inf = 1e9 + 7;
int n, m;
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};
int mx[N * 4], tag[N * 4];
const int L = 400000;
void pushdown(int k) {
  tag[k * 2] += tag[k];
  mx[k * 2] += tag[k];
  tag[k * 2 + 1] += tag[k];
  mx[k * 2 + 1] += tag[k];
  tag[k] = 0;
}
void build(int k, int le, int ri) {
  mx[k] = ri;
  if (le != ri) {
    int mid = (le + ri) / 2;
    build(k * 2, le, mid);
    build(k * 2 + 1, mid + 1, ri);
  }
}
void add(int k, int le, int ri, int pos, int delta) {
  if (ri <= pos) {
    mx[k] += delta;
    tag[k] += delta;
  } else {
    int mid = (le + ri) / 2;
    pushdown(k);
    add(k * 2, le, mid, pos, delta);
    if (pos > mid) add(k * 2 + 1, mid + 1, ri, pos, delta);
    mx[k] = max(mx[k * 2], mx[k * 2 + 1]);
  }
}
int getmax(int k, int le, int ri, int qr) {
  if (ri <= qr) {
    return mx[k];
  } else {
    int mid = (le + ri) / 2;
    pushdown(k);
    int res = getmax(k * 2, le, mid, qr);
    if (qr >= mid + 1) res = max(res, getmax(k * 2 + 1, mid + 1, ri, qr));
    return res;
  }
}
int main() {
  int n, k, m;
  n = getInt();
  k = getInt();
  m = getInt();
  build(1, 1, L);
  map<int, int> sp;
  set<pair<int, int> > st;
  for (int i = 1; i <= m; i++) {
    int x, y;
    x = getInt();
    y = getInt();
    int pos = y + abs(x - k);
    if (st.count(make_pair(x, y))) {
      st.erase(make_pair(x, y));
      sp[pos]--;
      if (sp[pos] == 0) sp.erase(pos);
      add(1, 1, L, pos, -1);
    } else {
      st.insert(make_pair(x, y));
      sp[pos]++;
      add(1, 1, L, pos, 1);
    }
    printf("%d\n", sp.size() == 0
                       ? 0
                       : max(0, getmax(1, 1, L, sp.rbegin()->first) - n - 1));
  }
}