Language: C++

#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>
#include <functional>
#include <set>
#include <ctime>
#include <random>
#include <chrono>
#include <cassert>
#include <tuple>
#include <utility>
using namespace std;

namespace {
  using Integer = long long; //__int128;
  template<class T, class S> istream& operator >> (istream& is, pair<T,S>& p){return is >> p.first >> p.second;}
  template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;}
  template<class T> istream& operator ,  (istream& is, T& val){ return is >> val;}
  template<class T, class S> ostream& operator << (ostream& os, const pair<T,S>& p){return os << p.first << " " << p.second;}
  template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(size_t i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;}
  template<class T> ostream& operator ,  (ostream& os, const T& val){ return os << " " << val;}

  template<class H> void print(const H& head){ cout << head; }
  template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); }
  template<class ... T> void println(const T& ... values){ print(values...); cout << endl; }

  template<class H> void eprint(const H& head){ cerr << head; }
  template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); }
  template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; }

  class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator   end(){ return range_iterator(  end_, step_); } };

  inline string operator "" _s (const char* str, size_t size){ return move(string(str)); }
  constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);}
  constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);}
  constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); }

  inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed

  mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count());

  template<class T> string join(const vector<T>& v, const string& sep){ stringstream ss; for(size_t i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str(); }

  inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; }
}
constexpr long long mod = 9_ten + 7;

array<array<int, 2000>, 2000> b0, b1, b2;

//accumulative_sum_2d acc(vec);
//acc(x0,y0, x1,y1); //[lb,ub]
class accumulative_sum_2d{
  using T=long long;
 public:
  vector<vector<T>> acc;
  template<class U>
  accumulative_sum_2d(const vector<vector<U>>& vec) : acc(vec.size(), vector<T>(vec.front().size(), 0)){
    for(size_t i=0; i<vec.size(); i++) for(size_t j=0; j<vec[i].size(); j++){
      acc[i][j] += vec[i][j] + (i?acc[i-1][j]:0) + (j?acc[i][j-1]:0) - (i&&j?acc[i-1][j-1]:0);
    }
  }

  template<size_t H, size_t W>
  accumulative_sum_2d(const array<array<int, W>, H>& vec) : acc(H, vector<T>(W, 0)){
    for(size_t i=0; i<vec.size(); i++) for(size_t j=0; j<vec[i].size(); j++){
      acc[i][j] += vec[i][j] + (i?acc[i-1][j]:0) + (j?acc[i][j-1]:0) - (i&&j?acc[i-1][j-1]:0);
    }
  }
  T operator () (int x_lb, int y_lb, int x_ub, int y_ub){
    return acc[y_ub][x_ub] - (y_lb?acc[y_lb-1][x_ub]:0) - (x_lb?acc[y_ub][x_lb-1]:0) + (x_lb&&y_lb?acc[y_lb-1][x_lb-1]:0);
  }
};

int main(){
  auto start_time = chrono::steady_clock::now();

  long long n,d;
  cin >> n,d;
  vector<pair<long long,long long>> p(n);
  cin >> p;

  map<pair<long long,long long>, long long> a;
  for(long long i=0; i<n; i++){
    long long y = p[i].first % d;
    long long x = p[i].second % d;
    a[{y,x}]++;
  }

  long long w = 0;
  for(auto p : a){
    long long c = p.second;
    long long d = ceil(sqrt(c));
    w = max(d, w);
  }
  w--;
  w = max(1ll, w);

  for(auto p : a){
    long long c = p.second;
    long long y = p.first.first;
    long long x = p.first.second;

    if(c <= w*w){
      b0[y][x]++;
      b0[y  ][x+d]++;
      b0[y+d][x  ]++;
      b0[y+d][x+d]++;
    }
    if(c <= w*(w+1)){
      b1[y][x]++;
      b1[y  ][x+d]++;
      b1[y+d][x  ]++;
      b1[y+d][x+d]++;
    }
    if(c <= (w+1)*(w+1)){
      b2[y][x]++;
      b2[y  ][x+d]++;
      b2[y+d][x  ]++;
      b2[y+d][x+d]++;
    }
  }

  accumulative_sum_2d c0(b0);
  accumulative_sum_2d c1(b1);
  accumulative_sum_2d c2(b2);

  // for(int y=0; y<2*d; y++) for(int x=0; x<2*d; x++){
  //   if(y) b0[y][x] += b0[y-1][x];
  //   if(x) b0[y][x] += b0[y][x-1];
  //   if(y&&x) b0[y][x] -= b0[y-1][x-1];

  //   if(y) b1[y][x] += b1[y-1][x];
  //   if(x) b1[y][x] += b1[y][x-1];
  //   if(y&&x) b1[y][x] -= b1[y-1][x-1];

  //   if(y) b2[y][x] += b2[y-1][x];
  //   if(x) b2[y][x] += b2[y][x-1];
  //   if(y&&x) b2[y][x] -= b2[y-1][x-1];
  // }

  long long ans = 1ll<<58;

  // w--;
  long long lb = -1;
  long long ub = d-1;

  auto check = [&](long long k){
    for(int y=0; y<d; y++) for(int x=0; x<d; x++){
    // for(auto p: a){
      int y = p.first.first;
      int x = p.first.second;

      int sum = 0;
      sum += c2(x, y, x+k, y+k);
      sum += c1(x+k+1, y, x+d-1, y+k);
      sum += c1(x, y+k+1, x+k, y+d-1);
      sum += c0(x+k+1, y+k+1, x+d-1, x+d-1);

      if(sum == a.size()){
        return true;
      }
    }
    return false;
  };
  while(ub-lb>1){
    long long mid = (lb+ub)/2;
    bool ok = check(mid);
    (ok? ub : lb) = mid;
  }
  println(w * d + ub);

  return 0;
}


Compiler output:
a.cc: In lambda function:
a.cc:156:17: error: 'class std::vector<std::pair<long long int, long long int> >' has no member named 'first'
  156 |       int y = p.first.first;
      |                 ^~~~~
a.cc:157:11: error: redeclaration of 'int x'
  157 |       int x = p.first.second;
      |           ^
a.cc:154:36: note: 'int x' previously declared here
  154 |     for(int y=0; y<d; y++) for(int x=0; x<d; x++){
      |                                    ^
a.cc:157:17: error: 'class std::vector<std::pair<long long int, long long int> >' has no member named 'first'
  157 |       int x = p.first.second;
      |                 ^~~~~