Problem: Niwango-kun, an employee of Dwango Co., Ltd., likes Niconico TV-chan, so he collected a lot of soft toys of her and spread them on the floor.

Niwango-kun has N black rare soft toys of Niconico TV-chan and they are spread together with ordinary ones. He wanted these black rare soft toys to be close together, so he decided to rearrange them.

In an infinitely large two-dimensional plane, every lattice point has a soft toy on it. The coordinates (x_i,y_i) of N black rare soft toys are given. All soft toys are considered to be points (without a length, area, or volume).

He may perform the following operation arbitrarily many times:

* Put an axis-aligned square with side length D, rotate the square by 90 degrees with four soft toys on the four corners of the square. More specifically, if the left bottom corner's coordinate is (x, y), rotate four points (x,y) \rightarrow (x+D,y) \rightarrow (x+D,y+D) \rightarrow (x,y+D) \rightarrow (x,y) in this order. Each of the four corners of the square must be on a lattice point.



Let's define the scatteredness of an arrangement by the minimum side length of an axis-aligned square enclosing all black rare soft toys. Black rare soft toys on the edges or the vertices of a square are considered to be enclosed by the square.

Find the minimum scatteredness after he performs arbitrarily many operations.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq D \leq 1000
* 0 \leq x_i, y_i \leq 10^9
* Given coordinates are pairwise distinct
* All numbers given in input are integers

Input

Input is given from Standard Input in the following format:


N D
x_1 y_1
:
x_N y_N


Output

Print the answer.

Examples

Input

3 1
0 0
1 0
2 0


Output

1


Input

19 2
1 3
2 3
0 1
1 1
2 1
3 1
4 4
5 4
6 4
7 4
8 4
8 3
8 2
8 1
8 0
7 0
6 0
5 0
4 0


Output

4


Input

8 3
0 0
0 3
3 0
3 3
2 2
2 5
5 2
5 5


Output

4

Solution (in CPP):

Solution:

#if 1
#include <iostream>
#include <fstream>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <queue>
#include <stack>
#include <array>
#include <deque>
#include <algorithm>
#include <utility>
#include <cstdint>
#include <functional>
#include <iomanip>
#include <numeric>
#include <assert.h>
#include <bitset>
#include <list>

auto& in = std::cin;
auto& out = std::cout;
#define all_range(C) std::begin(C), std::end(C)
const double PI = 3.141592653589793238462643383279502884197169399375105820974944;

int32_t N, D;

int32_t num[1000][1000];
int32_t square[1000][1000];
int32_t num_one[2100][2100];
int32_t num_error[2100][2100];


using INT_T = int32_t;
template<typename ARR>
inline void add_full(ARR& v1, ARR& v2)
{
	v1 += v2;
}
template<typename ARR, size_t N>
inline void add_full(ARR(&v1)[N], ARR(&v2)[N])
{
	auto iter1 = v1, iter2 = v2, iter1end = v1 + N;
	while (iter1 != iter1end) {
		add_full(*iter1++, *iter2++);
	}
}
//1-indexed累積和
template<size_t N>void CuSum(INT_T(&arr)[N])
{
	for (size_t i = 2; i < N; i++)
	{
		arr[i] += arr[i - 1];
	}
}
template<typename ARR, size_t N>void CuSum(ARR(&arr)[N])
{
	for (auto& arr2 : arr) {
		CuSum(arr2);
	}
	for (size_t i = 2; i < N; i++)
	{
		add_full(arr[i], arr[i - 1]);
	}
}
#if 0
template<size_t N, size_t M>void CuSum(INT_T(&arr)[N][M])
{
	for (auto& arr2 : arr) {
		CuSum(arr2);
	}

	for (size_t i = 2; i < N; i++)
	{
		add_full(arr[i], arr[i - 1]);
	}
}
template<size_t N, size_t M, size_t O>void CuSum(INT_T(&arr)[N][M][O])
{
	for (auto& arr2 : arr) {
		CuSum(arr2);
	}

	for (size_t i = 2; i < N; i++)
	{
		add_full(arr[i], arr[i - 1]);
	}
}
#endif
//1-indexed、(]区間
template<size_t N> INT_T get_sum(INT_T(&arr)[N], int x, int x2)
{
	return (arr[x2] - arr[x]);
}
//1-indexed、(]区間
template<size_t N, size_t M> INT_T get_sum(INT_T(&arr)[N][M], int x, int y, int x2, int y2)
{
	return (arr[y2][x2] - arr[y][x2] - arr[y2][x] + arr[y][x]);
}
//1-indexed、(]区間
template<size_t N, size_t M, size_t O> INT_T get_sum(INT_T(&arr)[N][M][O], int x, int y, int z, int x2, int y2, int z2)
{

	return arr(arr[z2][y2][x2] - arr[z][y2][x2] - arr[z2][y][x2] - arr[z2][y2][x] + arr[z2][y][x] + arr[z2][y][x] + arr[z][y][x2] - arr[z][y][x]);
}


int main()
{
	using std::get;
	using std::endl;
	in.sync_with_stdio(false);
	out.sync_with_stdio(false);
	in.tie(nullptr);
	out.tie(nullptr);

	in >> N >> D;

	for (size_t i = 0; i < N; i++)
	{
		int x, y;
		in >> x >> y;
		x %= D;
		y %= D;
		num[x][y]++;
	}

	int32_t max_square = -1;
	std::vector<std::tuple<int, int, int>> max_list;
	for (int32_t i = 0; i < D; i++)
	{
		for (int32_t j = 0; j < D; j++)
		{
			auto s = (int32_t)std::sqrt(square[i][j]);
			while ((s*s) < num[i][j]) {
				++s;
			}
			square[i][j] = s;
			int min_size = ((s*(s-1)) >= num[i][j])?1:0;
			if (max_square < s) {
				max_square = s;
				max_list.clear();
				max_list.emplace_back(i, j, min_size);
			}
			else if(max_square == s){
				max_list.emplace_back(i, j, min_size);
			}
		}
	}

	if (max_list.size() == 1)
	{
		out << (max_square - 1)*D << endl;
		return 0;
	}

	for (auto& i : max_list)
	{
		if (get<2>(i) == 1)
		{
			num_one[1+get<0>(i)][1+get<1>(i)]++;
			num_one[1+get<0>(i)][1+get<1>(i) + D]++;
			num_one[1+get<0>(i) + D][1 + get<1>(i)]++;
			num_one[1+get<0>(i)+D][1 + get<1>(i)+D]++;
		}
		else
		{
			num_error[1+get<0>(i)][1 + get<1>(i)]++;
			num_error[1+get<0>(i)][1 + get<1>(i) + D]++;
			num_error[1+get<0>(i) + D][1 + get<1>(i)]++;
			num_error[1+get<0>(i) + D][1 + get<1>(i) + D]++;
		}
	}
	CuSum(num_one);
	CuSum(num_error);

	using BS_INT = int32_t;
	BS_INT ok_range = D, ng_range = -1;
	while (std::abs(ok_range - ng_range) > 1) {
		BS_INT mid = (ok_range + ng_range) / 2;
		bool is_ok = false;

		for (int32_t i = 1-1; i <= D - 1; i++)
		{
			for (int32_t j = 1-1; j <= D - 1; j++)
			{
				if (get_sum(num_one, i + mid, j + mid, i + D, j + D) == 0 &&
					get_sum(num_error,i,j, i + D, j + D) - get_sum(num_error, i, j, i + mid, j + mid) == 0
					)
				{
					is_ok = true;
					goto break_2;
				}
			}
		}
	break_2:;



		//ここに書く

		if (is_ok) {
			ok_range = mid;
		}
		else {
			ng_range = mid;
		}
	}
	out << (max_square - 1)*D+ok_range-1 << endl;

#if 0
	std::vector<std::tuple<int, int, int>> max_list2;
	max_list2.reserve(max_list.size());
	for (auto& i : max_list) {
		max_list2.emplace_back(std::get<1>(i), std::get<0>(i), get<2>(i));
	}
	std::sort(max_list2.begin(), max_list2.end());


	int32_t min_diff = D;
	for (size_t i = 0; i < max_list.size(); i++)
	{
		if (i > 0 && get<0>(max_list[i]) == get<0>(max_list2[i-1])) { continue; }
		for (size_t j = 0; j < max_list2.size(); j++)
		{
			if (j > 0 && get<0>(max_list2[j]) == get<0>(max_list2[j-1])) { continue; }
			//for (auto& k : max_list)
			//{
			//	used[get<0>(k)][get<1>(k)] = false;
			//}

			auto cir_dec = [&max_list](size_t index) {if (index == 0) { return max_list.size() - 1; } else { return index - 1; }};
			auto cir_inc = [&max_list](size_t index) {if ((++index) == max_list.size()) { return (size_t)0; } else { return index; }};

			size_t k = cir_dec(i);
			for (; k != i; k = cir_dec(k))
			{
				if (get<2>(max_list[k]) == 0) {
					break;
				}
				used[get<0>(max_list[k])][get<1>(max_list[k])] = true;
			}
			size_t l = cir_dec(j);
			for (; k != i; k = cir_inc(k))
			{
				int32_t x_diff = get<0>(max_list[k]) - get<0>(max_list[i]);
				if (x_diff < 0) { x_diff += D; }

				while (get<2>(max_list2[l]) == 1 && used[get<1>(max_list2[l])][get<0>(max_list2[l])] == false && l != j);
				int32_t y_diff = get<0>(max_list[l]) - get<0>(max_list[j]);
				if (y_diff < 0) { y_diff += D; }

				min_diff = std::min(x_diff, y_diff);

				used[get<0>(max_list[k])][get<1>(max_list[k])] = false;
			}

#if 0
			for (size_t k = cir_dec(i); k != i; k= cir_dec(k))
			{
				int32_t x_diff = get<0>(max_list[k]) - get<0>(max_list[i]);
				if (x_diff < 0) { x_diff += D; }
				int32_t y_diff = 0;
				size_t l = cir_dec(j);
				while (get<2>(max_list2[l]) == 1 && used[get<1>(max_list2[l])][get<0>(max_list2[l])]==false && l != j);
				int32_t y_diff = get<0>(max_list[l]) - get<0>(max_list[l]);
				if (y_diff < 0) { y_diff += D; }

				if (get<2>(max_list[k]) == 0) {
					break;
				}
				used[get<0>(max_list[k])][get<1>(max_list[k])] = true;
			}
#endif
		}
	}
	out << (max_square - 1)*D + min_diff << endl;
#endif

	return 0;
}
#endif