// 私は猫です

#include<bits/stdc++.h>
#define ull unsigned long long
#define ll long long
#define pb push_back
#define mkp make_pair
#define fi first
#define se second
#define inf 1000000000
#define infll 1000000000000000000ll
#define pii pair<int,int>
#define rep(i,a,b,c) for(int i=(a);i<=(b);i+=(c))
#define per(i,a,b,c) for(int i=(a);i>=(b);i-=(c))
#define F(i,a,b) for(int i=a,i##end=b;i<=i##end;i++)
#define dF(i,a,b) for(int i=a,i##end=b;i>=i##end;i--)
#define cmh(sjy) while(sjy--)
#define lowbit(x) (x&(-x))
#define HH printf("\n")
#define eb emplace_back
#define poly vector<int>
#define SZ(x) ((int)x.size())
using namespace std;
ll read(){
	ll x=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-') f=-1;c=getchar();}
	while(c>='0'&&c<='9') x=(x<<3)+(x<<1)+(c^48),c=getchar();
	return x*f;
}
namespace Fastio{struct Reader{template<typename T>Reader&operator>>(T&x){x=0;short f=1;char c=getchar();while(c<'0'||c>'9'){if(c=='-')f*=-1;c=getchar();}while(c>='0'&&c<='9')x=(x<<3)+(x<<1)+(c^48),c=getchar();x*=f;return*this;}Reader&operator>>(double&x){x=0;double t=0;short f=1,s=0;char c=getchar();while((c<'0'||c>'9')&&c!='.'){if(c=='-')f*=-1;c=getchar();}while(c>='0'&&c<='9'&&c!='.')x=x*10+(c^48),c=getchar();if(c=='.')c=getchar();else{x*=f;return*this;}while(c>='0'&&c<='9')t=t*10+(c^48),s++,c=getchar();while(s--)t/=10.0;x=(x+t)*f;return*this;}Reader&operator>>(long double&x){x=0;long double t=0;short f=1,s=0;char c=getchar();while((c<'0'||c>'9')&&c!='.'){if(c=='-')f*=-1;c=getchar();}while(c>='0'&&c<='9'&&c!='.')x=x*10+(c^48),c=getchar();if(c=='.')c=getchar();else{x*=f;return*this;}while(c>='0'&&c<='9')t=t*10+(c^48),s++,c=getchar();while(s--)t/=10.0;x=(x+t)*f;return*this;}Reader&operator>>(__float128&x){x=0;__float128 t=0;short f=1,s=0;char c=getchar();while((c<'0'||c>'9')&&c!='.'){if(c=='-')f*=-1;c=getchar();}while(c>='0'&&c<='9'&&c!='.')x=x*10+(c^48),c=getchar();if(c=='.')c=getchar();else{x*=f;return*this;}while(c>='0'&&c<='9')t=t*10+(c^48),s++,c=getchar();while(s--)t/=10.0;x=(x+t)*f;return*this;}Reader&operator>>(char&c){c=getchar();while(c==' '||c=='\n'||c=='\r')c=getchar();return*this;}Reader&operator>>(char*str){int len=0;char c=getchar();while(c==' '||c=='\n'||c=='\r')c=getchar();while(c!=' '&&c!='\n'&&c!='\r')str[len++]=c,c=getchar();str[len]='\0';return*this;}Reader&operator>>(string&str){str.clear();char c=getchar();while(c==' '||c=='\n'||c=='\r')c=getchar();while(c!=' '&&c!='\n'&&c!='\r')str.push_back(c),c=getchar();return*this;}Reader(){}}cin;const char endl='\n';struct Writer{const int Setprecision=6;typedef int mxdouble;template<typename T>Writer&operator<<(T x){if(x==0){putchar('0');return*this;}if(x<0)putchar('-'),x=-x;static short sta[40];short top=0;while(x>0)sta[++top]=x%10,x/=10;while(top>0)putchar(sta[top]+'0'),top--;return*this;}Writer&operator<<(double x){if(x<0)putchar('-'),x=-x;mxdouble _=x;x-=(double)_;static short sta[40];short top=0;while(_>0)sta[++top]=_%10,_/=10;if(top==0)putchar('0');while(top>0)putchar(sta[top]+'0'),top--;putchar('.');for(int i=0;i<Setprecision;i++)x*=10;_=x;while(_>0)sta[++top]=_%10,_/=10;for(int i=0;i<Setprecision-top;i++)putchar('0');while(top>0)putchar(sta[top]+'0'),top--;return*this;}Writer&operator<<(long double x){if(x<0)putchar('-'),x=-x;mxdouble _=x;x-=(long double)_;static short sta[40];short top=0;while(_>0)sta[++top]=_%10,_/=10;if(top==0)putchar('0');while(top>0)putchar(sta[top]+'0'),top--;putchar('.');for(int i=0;i<Setprecision;i++)x*=10;_=x;while(_>0)sta[++top]=_%10,_/=10;for(int i=0;i<Setprecision-top;i++)putchar('0');while(top>0)putchar(sta[top]+'0'),top--;return*this;}Writer&operator<<(__float128 x){if(x<0)putchar('-'),x=-x;mxdouble _=x;x-=(__float128)_;static short sta[40];short top=0;while(_>0)sta[++top]=_%10,_/=10;if(top==0)putchar('0');while(top>0)putchar(sta[top]+'0'),top--;putchar('.');for(int i=0;i<Setprecision;i++)x*=10;_=x;while(_>0)sta[++top]=_%10,_/=10;for(int i=0;i<Setprecision-top;i++)putchar('0');while(top>0)putchar(sta[top]+'0'),top--;return*this;}Writer&operator<<(char c){putchar(c);return*this;}Writer&operator<<(char*str){int cur=0;while(str[cur])putchar(str[cur++]);return*this;}Writer&operator<<(const char*str){int cur=0;while(str[cur])putchar(str[cur++]);return*this;}Writer&operator<<(string str){int st=0,ed=str.size();while(st<ed)putchar(str[st++]);return*this;}Writer(){}}cout;}using namespace Fastio;
#define cin Fastio::cin
#define cout Fastio::cout
#define endl Fastio::endl
template<typename T>inline void chkmax(T &x,const T &y){ x=std::max(x,y); }
template<typename T>inline void chkmin(T &x,const T &y){ x=std::min(x,y); }
const int mod=1e9+7,maxn=200005;
inline int qpow(int x,ll y){
	int rt=1;
	for(;y;y>>=1,x=1ll*x*x%mod) if(y&1) rt=1ll*rt*x%mod;
	return rt;
}
inline void inc(int &x,const int y){ x=(x+y>=mod)?(x+y-mod):(x+y); }
inline void dec(int &x,const int y){ x=(x>=y)?(x-y):(x+mod-y); }
inline void mul(int &x,const int y){ x=1ll*x*y%mod; }
inline int add(const int x,const int y){ return (x+y>=mod)?(x+y-mod):(x+y); }
inline int sub(const int x,const int y){ return (x>=y)?(x-y):(x+mod-y); }
inline int prod(const int x,const int y){ return 1ll*x*y%mod; }
const int B=2000;
int n,m,zsy,typ,fa[maxn],siz[maxn];
int find(int x){ return fa[x]==x?x:fa[x]=find(fa[x]); }
vector<int>g[maxn],bel[maxn];
unordered_map<ll,int>mp;
ll gethash(int x,int y){ return 100003ll*x+y; }
int up[maxn],mx[maxn],sc[maxn],fr[maxn],f[maxn],dist[maxn],inv[maxn];
vector<int>qwq[maxn],pre[maxn];
void dfs(int u,int fa=0){
	vector<pii>tmp;
	for(auto v:g[u])if(v^fa)dfs(v,u),tmp.push_back(mkp(mx[v]+1,v));
	sort(tmp.begin(),tmp.end());
	if(!tmp.empty()){
		mx[u]=tmp.back().fi,fr[u]=tmp.back().se,tmp.pop_back();
		if(!tmp.empty())sc[u]=tmp.back().fi;	
	}
}
void dfs1(int u,int fa=0){
	f[u]=max(up[u],mx[u]);
	for(auto v:g[u])if(v^fa)up[v]=max(up[u],fr[u]==v?sc[u]:mx[u])+1,dfs1(v,u);
}
void Solve(int x,int y){
	if(x==y)return cout<<"-1"<<endl,void();
	if(mp.count(gethash(x,y)))return cout<<mp[gethash(x,y)]<<endl,void();
	if(siz[x]>siz[y])std::swap(x,y);
	int tmp=max(dist[x],dist[y]),res=0;
	F(i,0,siz[x]-1){
		const int p=upper_bound(qwq[y].begin(),qwq[y].end(),tmp-qwq[x][i]-1)-qwq[y].begin()-1;
		inc(res,1ll*tmp*(p+1)%mod);
		inc(res,sub(pre[y].back(),p<0?0:pre[y][p]));
		inc(res,1ll*(qwq[x][i]+1)*(siz[y]-1-p)%mod);
	}
	mul(res,inv[siz[x]]),mul(res,inv[siz[y]]),mp[gethash(x,y)]=mp[gethash(x,y)]=res;
	cout<<res<<endl;
}
void solve(){
	cin>>n>>m>>zsy>>typ;
	F(i,1,n)siz[fa[i]=i]=1,inv[i]=qpow(i,mod-2);
	F(i,1,m){
		int u,v; cin>>u>>v,g[u].push_back(v),g[v].push_back(u),u=find(u),v=find(v);
		if(u^v)siz[fa[u]=v]+=siz[u];
	}
	F(i,1,n)bel[find(i)].push_back(i);
	vector<int>vec,Roots;
	F(i,1,n)if(find(i)==i)Roots.push_back(i);
	for(auto i:Roots)if(siz[i]>=B)vec.push_back(i);
	for(auto R:Roots){
		dfs(R),dfs1(R);
		for(auto i:bel[R])qwq[R].push_back(f[i]);
		sort(qwq[R].begin(),qwq[R].end());
		int sum=0;
		F(i,0,siz[R]-1)inc(sum,qwq[R][i]),pre[R].push_back(sum);
		dist[R]=qwq[R].back();
	}
	for(auto x:vec)for(auto y:vec)if(x<y){
		int res=0,tmp=max(dist[x],dist[y]),p=siz[y]-1;
		F(i,0,siz[x]-1){
			for(;p>=0&&qwq[x][i]+qwq[y][p]+1>=tmp;--p);
			inc(res,1ll*tmp*(p+1)%mod);
			inc(res,sub(pre[y].back(),p<0?0:pre[y][p]));
			inc(res,1ll*(qwq[x][i]+1)*(siz[y]-1-p)%mod);
		}
		mul(res,inv[siz[x]]),mul(res,inv[siz[y]]),mp[gethash(x,y)]=mp[gethash(y,x)]=res;
	}
	F(i,1,zsy){
		int u,v; cin>>u>>v;
		Solve(find(u),find(v));
	}
}
signed main(){
	// ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
	int zsy=1;
	F(____,1,zsy)solve();
}