#pragma GCC optimize("Ofast,unroll-loops,-finline")
#include<bits/stdc++.h>
using namespace std;
const int NR=4e3+10;
const int MR=6e3+10;
const int M=3002;
#define int long long
const int MOD=1e9+7;
int n,m,a,b,x[NR],y[NR],fac[NR],ifac[NR];
int r1[MR],c1[MR],r2[MR],c2[MR],r3[MR],c3[MR];
void add(int &x,int y){x=(x+y)%MOD;}
void times(int &x,int y){x=x*y%MOD;}

int qpow(int x,int y){
	int res=1;
	while(y){
		if(y&1)res=res*x%MOD;
		x=x*x%MOD;y>>=1;
	}
	return res;
}
int Inv(int x){return qpow(x,MOD-2);}
int C(int x,int y){
	if(y<0||y>x)return 0;
	return fac[x]*ifac[y]%MOD*ifac[x-y]%MOD;
}

void solve(){
	for(int i=1,v1,v2;i<=n;i++){
		cin>>v1>>v2;
		x[i]=v1+v2+M;y[i]=v1-v2+M;
	}
	for(int i=0;i<=M*2;i++){
		r1[i]=r2[i]=r3[i]=1;
		for(int j=1;j<=a;j++)times(r1[i],C(m,(m+x[j]-i)/2));
		for(int j=a+1;j<=a+b;j++)times(r2[i],C(m,(m+x[j]-i)/2));
		for(int j=a+b+1;j<=n;j++)times(r3[i],C(m,(m+x[j]-i)/2));
	}
	for(int i=0;i<=M*2;i++){
		c1[i]=c2[i]=c3[i]=1;
		for(int j=1;j<=a;j++)times(c1[i],C(m,(m+y[j]-i)/2));
		for(int j=a+1;j<=a+b;j++)times(c2[i],C(m,(m+y[j]-i)/2));
		for(int j=a+b+1;j<=n;j++)times(c3[i],C(m,(m+y[j]-i)/2));
	}
	int res1=1,res2=1,res3=1;
	for(int i=2;i<=a;i++)
		if((x[i]&1)!=(x[1]&1)||(y[i]&1)!=(y[1]&1)){
			puts("0");
			return;
		}
	for(int i=a+2;i<=a+b;i++)
		if((x[i]&1)!=(x[a+1]&1)||(y[i]&1)!=(y[a+1]&1)){
			puts("0");
			return;
		}
	for(int i=a+b+1;i<=n;i++)
		if((x[i]&1)!=(x[a+b+1]&1)||(y[i]&1)!=(y[a+b+1]&1)){
			puts("0");
			return;
		}
	int sum1=0,sum2=0;
	for(int i=0;i<=M*2;i++)
		if((i&1)==((x[1]&1)^(m&1)))add(sum1,c1[i]);
		else c1[i]=0;
	for(int i=0;i<=M*2;i++)
		if((i&1)==((y[1]&1)^(m&1)))add(sum2,r1[i]);
		else r1[i]=0;
//	cout<<sum1<<" "<<sum2<<endl;
	res1=sum1*sum2%MOD;
	sum1=0,sum2=0;
	for(int i=0;i<=M*2;i++)
		if((i&1)==((x[a+1]&1)^(m&1)))add(sum1,c2[i]);
		else c2[i]=0;
	for(int i=0;i<=M*2;i++)
		if((i&1)==((y[a+1]&1)^(m&1)))add(sum2,r2[i]);
		else r2[i]=0;
//	cout<<sum1<<" "<<sum2<<endl;
	res2=sum1*sum2%MOD;
	sum1=0,sum2=0;
	for(int i=0;i<=M*2;i++)
		if((i&1)==((x[a+b+1]&1)^(m&1)))add(sum1,c3[i]);
		else c3[i]=0;
	for(int i=0;i<=M*2;i++)
		if((i&1)==((y[a+b+1]&1)^(m&1)))add(sum2,r3[i]);
		else r3[i]=0;
//	cout<<sum1<<" "<<sum2<<endl;
//	for(int i=0;i<=M*2;i++)
//		if(r1[i])printf("x:%lld %lld\n",i-M,r1[i]);
//	for(int i=0;i<=M*2;i++)
//		if(c1[i])printf("y:%lld %lld\n",i-M,c1[i]);
//	puts("----");
//	for(int i=0;i<=M*2;i++)
//		if(r3[i])printf("x:%lld %lld %lld\n",i-M,r3[i],C(m,(m+x[3]-i)/2));
//	for(int i=0;i<=M*2;i++)
//		if(c3[i])printf("y:%lld %lld\n",i-M,c3[i]);
	res3=sum1*sum2%MOD;
//	cout<<res1<<" "<<res2<<" "<<res3<<endl;
	int ans=res1*res2%MOD*res3%MOD;
	for(int i=0;i<=M*2;i++)
		for(int j=0;j<=M*2;j++)if((i+j)%2==0){
			int v1=r1[i]*c1[j]%MOD;
			int v2=r2[i]*c2[j]%MOD;
			int v3=r3[i]*c3[j]%MOD;
			if((i&1)!=((x[1]&1)^(m&1))||(j&1)!=((y[1]&1)^(m&1)))v1=0;
			if((i&1)!=((x[a+1]&1)^(m&1))||(j&1)!=((y[a+1]&1)^(m&1)))v2=0;
			if((i&1)!=((x[a+b+1]&1)^(m&1))||(j&1)!=((y[a+b+1]&1)^(m&1)))v3=0;
			if(!v1&&!v2&&!v3)continue;
//			printf("x:%lld y:%lld %lld %lld %lld\n",i-M,j-M,v1,v2,v3);
			add(ans,-v1*v2%MOD*res3);
			add(ans,-v1*v3%MOD*res2);
			add(ans,-v2*v3%MOD*res1);
			add(ans,v1*v2%MOD*v3);
		}
	cout<<(ans+MOD)%MOD<<endl;
}

signed main(){
	fac[0]=ifac[0]=1;
	for(int i=1;i<NR;i++)
		fac[i]=fac[i-1]*i%MOD,ifac[i]=ifac[i-1]*Inv(i)%MOD;
	while(cin>>n>>a>>b>>m)solve();
	return 0;
}