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:
#include <bits/stdc++.h>
#include <type_traits>
using namespace std;

using ll=int64_t;
#define int ll

#define FOR(i,a,b) for(int i=int(a);i<int(b);i++)
#define REP(i,b) FOR(i,0,b)
#define MP make_pair
#define PB push_back
#define EB emplace_back
#define ALL(x) x.begin(),x.end()
auto& errStream=cerr;
#ifdef LOCAL
#define cerr (cerr<<"-- line "<<__LINE__<<" -- ")
#else
class CerrDummy{}cerrDummy;
template<class T>
CerrDummy& operator<<(CerrDummy&cd,const T&){
	return cd;
}
using charTDummy=char;
using traitsDummy=char_traits<charTDummy>;
CerrDummy& operator<<(CerrDummy&cd,basic_ostream<charTDummy,traitsDummy>&(basic_ostream<charTDummy,traitsDummy>&)){
	return cd;
}
#define cerr cerrDummy
#endif
#define REACH cerr<<"reached"<<endl
#define DMP(x) cerr<<#x<<":"<<x<<endl
#define ZERO(x) memset(x,0,sizeof(x))
#define ONE(x) memset(x,-1,sizeof(x))

using pi=pair<int,int>;
using vi=vector<int>;
using ld=long double;

template<class T,class U>
ostream& operator<<(ostream& os,const pair<T,U>& p){
	os<<"("<<p.first<<","<<p.second<<")";
	return os;
}

template<class T>
ostream& operator <<(ostream& os,const vector<T>& v){
	os<<"{";
	REP(i,(int)v.size()){
		if(i)os<<",";
		os<<v[i];
	}
	os<<"}";
	return os;
}

ll read(){
	ll i;
	scanf("%"  SCNd64,&i);
	return i;
}

void printSpace(){
	printf(" ");
}

void printEoln(){
	printf("\n");
}

void print(ll x,int suc=1){
	printf("%" PRId64,x);
	if(suc==1)
		printEoln();
	if(suc==2)
		printSpace();
}

string readString(){
	static char buf[3341000];
	scanf("%s",buf);
	return string(buf);
}

char* readCharArray(){
	static char buf[3341000];
	static int bufUsed=0;
	char* ret=buf+bufUsed;
	scanf("%s",ret);
	bufUsed+=strlen(ret)+1;
	return ret;
}

template<class T,class U>
void chmax(T& a,U b){
	if(a<b)
		a=b;
}

template<class T,class U>
void chmin(T& a,U b){
	if(b<a)
		a=b;
}

template<class T>
T Sq(const T& t){
	return t*t;
}

#define CAPITAL
void Yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void No(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

const int Nmax=1010;
int d,buf[3][Nmax][Nmax];
int GetSum(int k,int y1,int y2,int x1,int x2){
	int res=buf[k][y2-1][x2-1];
	if(y1-1>=0)
		res-=buf[k][y1-1][x2-1];
	if(x1-1>=0)
		res-=buf[k][y2-1][x1-1];
	if(y1-1>=0&&x1-1>=0)
		res+=buf[k][y1-1][x1-1];
	return res;
}
int Wafrelka(int k,int y1,int y2,int x1,int x2){
	if(y2<=y1)return 0;
	if(x2<=x1)return 0;
	if(y1>=d){
		return Wafrelka(k,y1-d,y2-d,x1,x2);
	}
	if(x1>=d){
		return Wafrelka(k,y1,y2,x1-d,x2-d);
	}
	if(y2>d){
		return Wafrelka(k,y1,d,x1,x2)+Wafrelka(k,0,y2-d,x1,x2);
	}
	if(x2>d){
		return Wafrelka(k,y1,y2,x1,d)+Wafrelka(k,y1,y2,0,x2-d);
	}
	return GetSum(k,y1,y2,x1,x2);
}
void Prepare(int k){
	REP(y,d)REP(x,d)
		buf[k][y][x+1]+=buf[k][y][x];
	REP(y,d)REP(x,d)
		buf[k][y+1][x]+=buf[k][y][x];
}
bool Ok(const int mid,const vector<vi>&cnt){
	cerr<<mid<<endl;
	ZERO(buf);
	int p=mid/d;
	int q=d-mid%d;
	REP(y,d)REP(x,d){
		if(cnt[y][x]<=p*p){
			cerr<<0<<endl;
			buf[0][y][x]++;
		}else if(cnt[y][x]<=p*(p+1)){
			cerr<<1<<endl;
			buf[1][y][x]++;
		}else if(cnt[y][x]<=(p+1)*(p+1)){
			cerr<<2<<endl;
			buf[2][y][x]++;
		}else
			return false;
	}
	REP(k,3)
		Prepare(k);
	REP(y,d)REP(x,d){
		int a00=Wafrelka(1,y,y+q,x,x+q)+Wafrelka(2,y,y+q,x,x+q);
		int a01=Wafrelka(2,y,y+q,x+q,x+d);
		int a10=Wafrelka(2,y+q,y+d,x,x+q);
		if(a00==0&&a01==0&&a10==0)
			return true;
	}
	return false;
}

signed main(){
	int n=read();
	d=read();
	vector<vi> cnt(d,vi(d,0));
	REP(i,n){
		int x=read(),y=read();
		cnt[y%d][x%d]++;
	}
	int low=0,high=d*n;
	while(high-low>1){
		const int mid=(low+high)/2;
		if(Ok(mid,cnt)){
			high=mid;
		}else{
			low=mid;
		}
	}
	print(high-1);
}