#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
#define il inline
#define LL long long
#define _(d) while(d(isdigit(ch=getchar())))
using namespace std;
const int N=1e5+5,p=1e9+7;
LL jc[N<<1],ny[N<<1],ans;
struct node{int x,y;}pi[2005];
int n,m,k,tmp,num,s,f[2005][25];
il int read(){int x,f=1;char ch;_(!)ch=='-'?f=-1:f;x=ch^48;_()x=(x<<1)+(x<<3)+(ch^48);return f*x;}
bool cmp(node t1,node t2){return (t1.x<t2.x||(t1.x==t2.x)&&t1.y<t2.y);}
il LL ksm(LL a,int y){LL b=1;while(y){if(y&1)b=b*a%p;a=a*a%p;y>>=1;}return b;}
il LL C(int n,int m){return jc[n]*ny[m]%p*ny[n-m]%p;}
il LL way(int i,int j){int x=pi[j].x-pi[i].x,y=pi[j].y-pi[i].y;return C(x+y,x);
}
int main()
{n=read();m=read();k=read();tmp=read();s=tmp;for(int i=1;i<=k;i++)pi[i].x=read(),pi[i].y=read();sort(pi+1,pi+1+k,cmp);pi[++k].x=n;pi[k].y=m;int kk=n+m;jc[0]=1;for(int i=1;i<=kk;i++)jc[i]=jc[i-1]*(LL)i%p;ny[kk]=ksm(jc[kk],p-2);for(int i=kk;i;i--)ny[i-1]=ny[i]*(LL)i%p;num=0;/*tmp=(tmp+1)>>1;*/while(tmp>1){num++;tmp=(tmp+1)>>1;}for(int i=1;i<=k;i++){for(int j=0;j<=num;j++){f[i][j]=C(pi[i].x+pi[i].y-2,pi[i].x-1);for(int kk=1;kk<i;kk++){if(pi[kk].y>pi[i].y)continue;f[i][j]=((f[i][j]-f[kk][j]*way(kk,i)%p)%p+p)%p;}for(int kk=1;kk<j;kk++){f[i][j]=((f[i][j]-f[i][kk])%p+p)%p;}}
//      f[i][num]=C(pi[i].x+pi[i].y-2,pi[i].x-1);
//      for(int j=num;j>=1;j--)f[i][j]=((f[i][j]-f[i][j-1])%p+p)%p;printf("%d ",s);
    }for(int i=1;i<=num;i++){ans=(ans+(LL)s*f[k][i]%p)%p;s=(s+1)>>1;}LL sum=C(n+m-2,n-1);for(int i=1;i<=num;i++)sum=(sum-f[k][i]+p)%p;ans=(ans+sum)%p;ans=ans*ksm(C(n+m-2,n-1),p-2)%p;printf("%lld\n",ans);return 0;
}