#include <bits/stdc++.h>
using namespace std;
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  os << '{';
  string sep;
  for (const auto &x : v) os << sep << x, sep = ", ";
  return os << '}';
}
template <typename T, size_t size>
ostream &operator<<(ostream &os, const array<T, size> &arr) {
  os << '{';
  string sep;
  for (const auto &x : arr) os << sep << x, sep = ", ";
  return os << '}';
}
template <typename A, typename B>
ostream &operator<<(ostream &os, const pair<A, B> &p) {
  return os << '(' << p.first << ", " << p.second << ')';
}
void dbg_out() { cerr << endl; }
template <typename Head, typename... Tail>
void dbg_out(Head H, Tail... T) {
  cerr << ' ' << H;
  dbg_out(T...);
}
using T_tree = int;
const T_tree T_INF = numeric_limits<T_tree>::max() / 2;
struct segment_change {
  T_tree to_add;
  segment_change(T_tree _to_add = 0) : to_add(_to_add) {}
};
struct segment {
  T_tree max_prefix, sum;
  segment(T_tree _max_prefix = -T_INF, T_tree _sum = 0)
      : max_prefix(_max_prefix), sum(_sum) {}
  void apply(const segment_change &change) {
    max_prefix += change.to_add;
    sum += change.to_add;
  }
  void join(const segment &other) {
    max_prefix = max(max_prefix, sum + other.max_prefix);
    sum += other.sum;
  }
  void join(const segment &a, const segment &b) {
    *this = a;
    join(b);
  }
};
int right_half[32];
struct max_prefix_sum_tree {
  static const bool POWER_OF_TWO_MODE = true;
  int tree_n = 0;
  vector<segment> tree;
  max_prefix_sum_tree(int n = -1) {
    if (n >= 0) init(n);
  }
  void init(int n) {
    if (POWER_OF_TWO_MODE) {
      tree_n = 1;
      while (tree_n < n) tree_n *= 2;
    } else {
      tree_n = n;
    }
    tree.assign(2 * tree_n, segment());
  }
  void build(const vector<segment> &initial) {
    int n = int(initial.size());
    init(n);
    assert(n <= tree_n);
    for (int i = 0; i < n; i++) tree[tree_n + i] = initial[i];
    for (int position = tree_n - 1; position > 0; position--)
      tree[position].join(tree[2 * position], tree[2 * position + 1]);
  }
  segment query(int a, int b) const {
    assert(0 <= a && a <= b && b <= tree_n);
    segment answer;
    int r_size = 0;
    for (a += tree_n, b += tree_n; a < b; a /= 2, b /= 2) {
      if (a & 1) answer.join(tree[a++]);
      if (b & 1) right_half[r_size++] = --b;
    }
    for (int i = r_size - 1; i >= 0; i--) answer.join(tree[right_half[i]]);
    return answer;
  }
  segment query_single(int index) const {
    assert(0 <= index && index < tree_n);
    return tree[tree_n + index];
  }
  void join_up(int position) {
    while (position > 1) {
      position /= 2;
      tree[position].join(tree[2 * position], tree[2 * position + 1]);
    }
  }
  void update(int index, const segment_change &change) {
    assert(0 <= index && index < tree_n);
    int position = tree_n + index;
    tree[position].apply(change);
    join_up(position);
  }
  void update(int index, const segment &seg) {
    assert(0 <= index && index < tree_n);
    int position = tree_n + index;
    tree[position] = seg;
    join_up(position);
  }
};
struct add_max_seg_tree {
  max_prefix_sum_tree tree;
  add_max_seg_tree(int n = -1) {
    if (n >= 0) init(n);
  }
  void init(int n) { tree.init(n); }
  void build(const vector<T_tree> &initial) {
    vector<segment> segment_initial(initial.size());
    T_tree previous = 0;
    for (int i = 0; i < int(initial.size()); i++) {
      T_tree value = initial[i] - previous;
      previous = initial[i];
      segment_initial[i] = segment(value, value);
    }
    tree.build(segment_initial);
  }
  T_tree query(int a, int b) const {
    return tree.query(0, a).sum + tree.query(a, b).max_prefix;
  }
  T_tree query_full() const { return tree.tree[1].max_prefix; }
  void update(int a, int b, segment_change change) {
    if (a < tree.tree_n) tree.update(a, change);
    if (b < tree.tree_n) {
      change.to_add *= -1;
      tree.update(b, change);
    }
  }
  void set_value(int index, T_tree value) {
    T_tree current = query(index, index + 1);
    update(index, index + 1, segment_change(value - current));
  }
};
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int N, K, M;
  cin >> N >> K >> M;
  K--;
  add_max_seg_tree tree(2 * N);
  vector<int> initial(2 * N);
  for (int i = 0; i < 2 * N; i++) initial[i] = i;
  tree.build(initial);
  map<array<int, 2>, int> pawns;
  multiset<int> coords;
  for (int i = 0; i < M; i++) {
    int x, y;
    cin >> x >> y;
    x--;
    y--;
    int status = pawns[{x, y}]++ % 2;
    status = status == 0 ? +1 : -1;
    int coordinate = y + abs(x - K);
    if (status > 0)
      coords.insert(coordinate);
    else
      coords.erase(coords.find(coordinate));
    tree.update(0, coordinate + 1, segment_change(status));
    int answer = 0;
    if (!coords.empty())
      answer = max(tree.query(0, *coords.rbegin() + 1) - N, 0);
    cout << answer << '\n';
  }
}

### Prompt

Your challenge is to write a cpp solution to the following 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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  os << '{';
  string sep;
  for (const auto &x : v) os << sep << x, sep = ", ";
  return os << '}';
}
template <typename T, size_t size>
ostream &operator<<(ostream &os, const array<T, size> &arr) {
  os << '{';
  string sep;
  for (const auto &x : arr) os << sep << x, sep = ", ";
  return os << '}';
}
template <typename A, typename B>
ostream &operator<<(ostream &os, const pair<A, B> &p) {
  return os << '(' << p.first << ", " << p.second << ')';
}
void dbg_out() { cerr << endl; }
template <typename Head, typename... Tail>
void dbg_out(Head H, Tail... T) {
  cerr << ' ' << H;
  dbg_out(T...);
}
using T_tree = int;
const T_tree T_INF = numeric_limits<T_tree>::max() / 2;
struct segment_change {
  T_tree to_add;
  segment_change(T_tree _to_add = 0) : to_add(_to_add) {}
};
struct segment {
  T_tree max_prefix, sum;
  segment(T_tree _max_prefix = -T_INF, T_tree _sum = 0)
      : max_prefix(_max_prefix), sum(_sum) {}
  void apply(const segment_change &change) {
    max_prefix += change.to_add;
    sum += change.to_add;
  }
  void join(const segment &other) {
    max_prefix = max(max_prefix, sum + other.max_prefix);
    sum += other.sum;
  }
  void join(const segment &a, const segment &b) {
    *this = a;
    join(b);
  }
};
int right_half[32];
struct max_prefix_sum_tree {
  static const bool POWER_OF_TWO_MODE = true;
  int tree_n = 0;
  vector<segment> tree;
  max_prefix_sum_tree(int n = -1) {
    if (n >= 0) init(n);
  }
  void init(int n) {
    if (POWER_OF_TWO_MODE) {
      tree_n = 1;
      while (tree_n < n) tree_n *= 2;
    } else {
      tree_n = n;
    }
    tree.assign(2 * tree_n, segment());
  }
  void build(const vector<segment> &initial) {
    int n = int(initial.size());
    init(n);
    assert(n <= tree_n);
    for (int i = 0; i < n; i++) tree[tree_n + i] = initial[i];
    for (int position = tree_n - 1; position > 0; position--)
      tree[position].join(tree[2 * position], tree[2 * position + 1]);
  }
  segment query(int a, int b) const {
    assert(0 <= a && a <= b && b <= tree_n);
    segment answer;
    int r_size = 0;
    for (a += tree_n, b += tree_n; a < b; a /= 2, b /= 2) {
      if (a & 1) answer.join(tree[a++]);
      if (b & 1) right_half[r_size++] = --b;
    }
    for (int i = r_size - 1; i >= 0; i--) answer.join(tree[right_half[i]]);
    return answer;
  }
  segment query_single(int index) const {
    assert(0 <= index && index < tree_n);
    return tree[tree_n + index];
  }
  void join_up(int position) {
    while (position > 1) {
      position /= 2;
      tree[position].join(tree[2 * position], tree[2 * position + 1]);
    }
  }
  void update(int index, const segment_change &change) {
    assert(0 <= index && index < tree_n);
    int position = tree_n + index;
    tree[position].apply(change);
    join_up(position);
  }
  void update(int index, const segment &seg) {
    assert(0 <= index && index < tree_n);
    int position = tree_n + index;
    tree[position] = seg;
    join_up(position);
  }
};
struct add_max_seg_tree {
  max_prefix_sum_tree tree;
  add_max_seg_tree(int n = -1) {
    if (n >= 0) init(n);
  }
  void init(int n) { tree.init(n); }
  void build(const vector<T_tree> &initial) {
    vector<segment> segment_initial(initial.size());
    T_tree previous = 0;
    for (int i = 0; i < int(initial.size()); i++) {
      T_tree value = initial[i] - previous;
      previous = initial[i];
      segment_initial[i] = segment(value, value);
    }
    tree.build(segment_initial);
  }
  T_tree query(int a, int b) const {
    return tree.query(0, a).sum + tree.query(a, b).max_prefix;
  }
  T_tree query_full() const { return tree.tree[1].max_prefix; }
  void update(int a, int b, segment_change change) {
    if (a < tree.tree_n) tree.update(a, change);
    if (b < tree.tree_n) {
      change.to_add *= -1;
      tree.update(b, change);
    }
  }
  void set_value(int index, T_tree value) {
    T_tree current = query(index, index + 1);
    update(index, index + 1, segment_change(value - current));
  }
};
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int N, K, M;
  cin >> N >> K >> M;
  K--;
  add_max_seg_tree tree(2 * N);
  vector<int> initial(2 * N);
  for (int i = 0; i < 2 * N; i++) initial[i] = i;
  tree.build(initial);
  map<array<int, 2>, int> pawns;
  multiset<int> coords;
  for (int i = 0; i < M; i++) {
    int x, y;
    cin >> x >> y;
    x--;
    y--;
    int status = pawns[{x, y}]++ % 2;
    status = status == 0 ? +1 : -1;
    int coordinate = y + abs(x - K);
    if (status > 0)
      coords.insert(coordinate);
    else
      coords.erase(coords.find(coordinate));
    tree.update(0, coordinate + 1, segment_change(status));
    int answer = 0;
    if (!coords.empty())
      answer = max(tree.query(0, *coords.rbegin() + 1) - N, 0);
    cout << answer << '\n';
  }
}

```