#include <bits/stdc++.h>
using namespace std;
const double pi = acos(0.0) * 2.0;
const long double eps = 1e-10;
const int step[8][2] = {{-1, 0}, {0, 1}, {1, 0},  {0, -1},
                        {-1, 1}, {1, 1}, {1, -1}, {-1, -1}};
template <class T>
inline T abs1(T a) {
  return a < 0 ? -a : a;
}
template <typename t, typename t1>
t min1(t a, t1 b) {
  return a < b ? a : b;
}
template <typename t, typename... arg>
t min1(t a, arg... arr) {
  return min1(a, min1(arr...));
}
template <typename t, typename t1>
t max1(t a, t1 b) {
  return a > b ? a : b;
}
template <typename t, typename... arg>
t max1(t a, arg... arr) {
  return max1(a, max1(arr...));
}
inline int jud(double a, double b) {
  if (abs(a) < eps && abs(b) < eps)
    return 0;
  else if (abs1(a - b) / max(abs1(a), abs1(b)) < eps)
    return 0;
  if (a < b) return -1;
  return 1;
}
template <typename t>
inline int jud(t a, t b) {
  if (a < b) return -1;
  if (a == b) return 0;
  return 1;
}
template <typename it, typename t1>
inline int find(t1 val, it a, int na, bool f_small = 1, bool f_lb = 1) {
  if (na == 0) return 0;
  int be = 0, en = na - 1;
  if (*a <= *(a + na - 1)) {
    if (f_lb == 0)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(*(a + mid), val) != 1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(*(a + mid), val) != -1)
          en = mid;
        else
          be = mid + 1;
      }
    if (f_small && jud(*(a + be), val) == 1) be--;
    if (!f_small && jud(*(a + be), val) == -1) be++;
  } else {
    if (f_lb)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(*(a + mid), val) != -1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(*(a + mid), val) != 1)
          en = mid;
        else
          be = mid + 1;
      }
    if (!f_small && jud(*(a + be), val) == -1) be--;
    if (f_small && jud(*(a + be), val) == 1) be++;
  }
  return be;
}
template <class T>
inline T lowb(T num) {
  return num & (-num);
}
inline int bitnum(unsigned int nValue) { return __builtin_popcount(nValue); }
inline int bitnum(int nValue) { return __builtin_popcount(nValue); }
inline int bitnum(unsigned long long nValue) {
  return __builtin_popcount(nValue) + __builtin_popcount(nValue >> 32);
}
inline int bitnum(long long nValue) {
  return __builtin_popcount(nValue) + __builtin_popcount(nValue >> 32);
}
inline int bitmaxl(unsigned int a) {
  if (a == 0) return 0;
  return 32 - __builtin_clz(a);
}
inline int bitmaxl(int a) {
  if (a == 0) return 0;
  return 32 - __builtin_clz(a);
}
inline int bitmaxl(unsigned long long a) {
  int temp = a >> 32;
  if (temp) return 32 - __builtin_clz(temp) + 32;
  return bitmaxl(int(a));
}
inline int bitmaxl(long long a) {
  int temp = a >> 32;
  if (temp) return 32 - __builtin_clz(temp) + 32;
  return bitmaxl(int(a));
}
long long pow(long long n, long long m, long long mod = 0) {
  if (m < 0) return 0;
  long long ans = 1;
  long long k = n;
  while (m) {
    if (m & 1) {
      ans *= k;
      if (mod) ans %= mod;
    }
    k *= k;
    if (mod) k %= mod;
    m >>= 1;
  }
  return ans;
}
template <class t1, class t2>
inline void add(t1 &a, t2 b, int mod = -1) {
  if (mod == -1) mod = 1000000007;
  a += b;
  while (a >= mod) a -= mod;
  while (a < 0) a += mod;
}
template <class t>
void output1(t arr) {
  for (int i = 0; i < (int)arr.size(); i++) cerr << arr[i] << ' ';
  cerr << endl;
}
template <class t>
void output2(t arr) {
  for (int i = 0; i < (int)arr.size(); i++) output1(arr[i]);
}
const int maxn = 100100;
int n, k;
int cnt[maxn * 2];
int arr[maxn], larr;
pair<int, int> orig[maxn];
pair<pair<int, int>, int> event[maxn * 2];
int stat[maxn * 2], last[maxn * 2];
long long ans[maxn];
int main() {
  ios_base::sync_with_stdio(0);
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; i++) {
    scanf("%d%d", &orig[i].first, &orig[i].second);
    arr[larr++] = orig[i].second;
    arr[larr++] = orig[i].second + k;
    event[i * 2] = make_pair(orig[i], 1);
    event[i * 2 + 1] =
        make_pair(make_pair(orig[i].first + k, orig[i].second), -1);
  }
  sort(event, event + 2 * n);
  sort(arr, arr + larr);
  larr = unique(arr, arr + larr) - arr;
  memset(last, 0x3f, sizeof(last));
  for (int i = 0; i < 2 * n; i++) {
    int no = find(event[i].first.second, arr, larr);
    for (int rno = no; rno < larr - 1 && arr[rno] < arr[no] + k; rno++) {
      if (last[rno] < event[i].first.first)
        ans[stat[rno]] += 1ll * (event[i].first.first - last[rno]) *
                          (arr[rno + 1] - arr[rno]);
      last[rno] = event[i].first.first;
      if (event[i].second == -1)
        stat[rno]--;
      else
        stat[rno]++;
    }
  }
  for (int i = 1; i <= n; i++) printf("%I64d\n", ans[i]);
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

Snow Queen told Kay to form a word "eternity" using pieces of ice. Kay is eager to deal with the task, because he will then become free, and Snow Queen will give him all the world and a pair of skates.

Behind the palace of the Snow Queen there is an infinite field consisting of cells. There are n pieces of ice spread over the field, each piece occupying exactly one cell and no two pieces occupying the same cell. To estimate the difficulty of the task Kay looks at some squares of size k × k cells, with corners located at the corners of the cells and sides parallel to coordinate axis and counts the number of pieces of the ice inside them.

This method gives an estimation of the difficulty of some part of the field. However, Kay also wants to estimate the total difficulty, so he came up with the following criteria: for each x (1 ≤ x ≤ n) he wants to count the number of squares of size k × k, such that there are exactly x pieces of the ice inside.

Please, help Kay estimate the difficulty of the task given by the Snow Queen.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 100 000, 1 ≤ k ≤ 300) — the number of pieces of the ice and the value k, respectively. Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109) — coordinates of the cell containing i-th piece of the ice. It's guaranteed, that no two pieces of the ice occupy the same cell.

Output

Print n integers: the number of squares of size k × k containing exactly 1, 2, ..., n pieces of the ice.

Example

Input

5 3
4 5
4 6
5 5
5 6
7 7


Output

10 8 1 4 0 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const double pi = acos(0.0) * 2.0;
const long double eps = 1e-10;
const int step[8][2] = {{-1, 0}, {0, 1}, {1, 0},  {0, -1},
                        {-1, 1}, {1, 1}, {1, -1}, {-1, -1}};
template <class T>
inline T abs1(T a) {
  return a < 0 ? -a : a;
}
template <typename t, typename t1>
t min1(t a, t1 b) {
  return a < b ? a : b;
}
template <typename t, typename... arg>
t min1(t a, arg... arr) {
  return min1(a, min1(arr...));
}
template <typename t, typename t1>
t max1(t a, t1 b) {
  return a > b ? a : b;
}
template <typename t, typename... arg>
t max1(t a, arg... arr) {
  return max1(a, max1(arr...));
}
inline int jud(double a, double b) {
  if (abs(a) < eps && abs(b) < eps)
    return 0;
  else if (abs1(a - b) / max(abs1(a), abs1(b)) < eps)
    return 0;
  if (a < b) return -1;
  return 1;
}
template <typename t>
inline int jud(t a, t b) {
  if (a < b) return -1;
  if (a == b) return 0;
  return 1;
}
template <typename it, typename t1>
inline int find(t1 val, it a, int na, bool f_small = 1, bool f_lb = 1) {
  if (na == 0) return 0;
  int be = 0, en = na - 1;
  if (*a <= *(a + na - 1)) {
    if (f_lb == 0)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(*(a + mid), val) != 1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(*(a + mid), val) != -1)
          en = mid;
        else
          be = mid + 1;
      }
    if (f_small && jud(*(a + be), val) == 1) be--;
    if (!f_small && jud(*(a + be), val) == -1) be++;
  } else {
    if (f_lb)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(*(a + mid), val) != -1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(*(a + mid), val) != 1)
          en = mid;
        else
          be = mid + 1;
      }
    if (!f_small && jud(*(a + be), val) == -1) be--;
    if (f_small && jud(*(a + be), val) == 1) be++;
  }
  return be;
}
template <class T>
inline T lowb(T num) {
  return num & (-num);
}
inline int bitnum(unsigned int nValue) { return __builtin_popcount(nValue); }
inline int bitnum(int nValue) { return __builtin_popcount(nValue); }
inline int bitnum(unsigned long long nValue) {
  return __builtin_popcount(nValue) + __builtin_popcount(nValue >> 32);
}
inline int bitnum(long long nValue) {
  return __builtin_popcount(nValue) + __builtin_popcount(nValue >> 32);
}
inline int bitmaxl(unsigned int a) {
  if (a == 0) return 0;
  return 32 - __builtin_clz(a);
}
inline int bitmaxl(int a) {
  if (a == 0) return 0;
  return 32 - __builtin_clz(a);
}
inline int bitmaxl(unsigned long long a) {
  int temp = a >> 32;
  if (temp) return 32 - __builtin_clz(temp) + 32;
  return bitmaxl(int(a));
}
inline int bitmaxl(long long a) {
  int temp = a >> 32;
  if (temp) return 32 - __builtin_clz(temp) + 32;
  return bitmaxl(int(a));
}
long long pow(long long n, long long m, long long mod = 0) {
  if (m < 0) return 0;
  long long ans = 1;
  long long k = n;
  while (m) {
    if (m & 1) {
      ans *= k;
      if (mod) ans %= mod;
    }
    k *= k;
    if (mod) k %= mod;
    m >>= 1;
  }
  return ans;
}
template <class t1, class t2>
inline void add(t1 &a, t2 b, int mod = -1) {
  if (mod == -1) mod = 1000000007;
  a += b;
  while (a >= mod) a -= mod;
  while (a < 0) a += mod;
}
template <class t>
void output1(t arr) {
  for (int i = 0; i < (int)arr.size(); i++) cerr << arr[i] << ' ';
  cerr << endl;
}
template <class t>
void output2(t arr) {
  for (int i = 0; i < (int)arr.size(); i++) output1(arr[i]);
}
const int maxn = 100100;
int n, k;
int cnt[maxn * 2];
int arr[maxn], larr;
pair<int, int> orig[maxn];
pair<pair<int, int>, int> event[maxn * 2];
int stat[maxn * 2], last[maxn * 2];
long long ans[maxn];
int main() {
  ios_base::sync_with_stdio(0);
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; i++) {
    scanf("%d%d", &orig[i].first, &orig[i].second);
    arr[larr++] = orig[i].second;
    arr[larr++] = orig[i].second + k;
    event[i * 2] = make_pair(orig[i], 1);
    event[i * 2 + 1] =
        make_pair(make_pair(orig[i].first + k, orig[i].second), -1);
  }
  sort(event, event + 2 * n);
  sort(arr, arr + larr);
  larr = unique(arr, arr + larr) - arr;
  memset(last, 0x3f, sizeof(last));
  for (int i = 0; i < 2 * n; i++) {
    int no = find(event[i].first.second, arr, larr);
    for (int rno = no; rno < larr - 1 && arr[rno] < arr[no] + k; rno++) {
      if (last[rno] < event[i].first.first)
        ans[stat[rno]] += 1ll * (event[i].first.first - last[rno]) *
                          (arr[rno + 1] - arr[rno]);
      last[rno] = event[i].first.first;
      if (event[i].second == -1)
        stat[rno]--;
      else
        stat[rno]++;
    }
  }
  for (int i = 1; i <= n; i++) printf("%I64d\n", ans[i]);
  return 0;
}

```