#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 100;
const int mod = 1e9 + 7;
vector<int> d[N], g[N];
int rr[N], iv[N], ss[N];
int calc(int u, int v){
    int Mn = max(rr[u], rr[v]);
    //cerr << "calc " << u << " " << v << " Mn = " << Mn << endl;
    int lu = d[u].size(), lv = d[v].size();
    ss[lu] = 0;for(int i = lu - 1;i >= 0;i--) ss[i] = (ss[i + 1] + d[u][i]) % mod;
    //cerr << u << " ss:";
    //for(int i = 0;i <= lu;i++) cerr << ss[i] << " ";
    //cerr << endl;
    int pu = 0, Sum = 0;
    for(int pv = lv - 1;pv >= 0;pv--){
        while(pu < lu && d[u][pu] + d[v][pv] + 1 < Mn)
            pu++;
        //cerr << pv << " - " << pu << ":" << d[u][pu] + d[v][pv] + 1 << endl;
        int cnt = lu - pu;
        Sum = (Sum + (1ll * pu * Mn % mod + 1ll * cnt * (d[v][pv] + 1) % mod + ss[pu]) % mod) % mod;
    }
    return 1ll * Sum * iv[lu] % mod * iv[lv] % mod;
}
int siz[N], scnt;
int col[N], Mx[N], ft, fat[N], fd[N];
bool ban[N];
void dfs1(int u, int fa){
    col[u] = scnt;
    for(int v : g[u]) if(v != fa){
        Mx[v] = Mx[u] + 1;
        if(Mx[v] > Mx[ft]) ft = v;
        dfs1(v, u);
    }
}
void dfs2(int u, int fa){
    for(int v : g[u]) if(v != fa){
        Mx[v] = Mx[u] + 1;
        fat[v] = u;
        if(Mx[v] > Mx[ft]) ft = v;
        dfs2(v, u);
    }
}
void dfs3(int u, int fa){
    for(int v : g[u]) if(v != fa && !ban[v]){
        //cerr << v << " ";
        fd[v] = fd[u] + 1;
        d[scnt].push_back(fd[v]);
        dfs3(v, u);
    }
}
int ans[N];
struct Qrys{
    int v, id;
};
vector<Qrys> qs[N];
unordered_map<int, int> rs[N];
int main(){
    ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    int n, m, q, tp;
    cin >> n >> m >> q >> tp;
    iv[1] = 1;for(int i = 2;i <= n;i++) iv[i] = 1ll * (mod - mod / i) * iv[mod % i] % mod;
    for(int i = 1;i <= m;i++){
        int x, y;cin >> x >> y;
        g[x].push_back(y);
        g[y].push_back(x);
    }
    for(int i = 1, u, v;i <= n;i++) if(!col[i]){
        ++scnt;Mx[ft = i] = 0;
        dfs1(i, i);
        Mx[v = ft] = 0;
        fat[v] = v;
        dfs2(v, v);
        u = ft;
        int x = u, len = 0, cur = 0;
        while(1){
            len++, ban[x] = 1;
            if(x == fat[x]) break;
            x = fat[x];
        }
        rr[scnt] = len - 1;
        x = u;
        //cerr << "scc " << scnt << ":r = " << rr[scnt] << endl;
        //cerr << "Members:";
        while(1){
            fd[x] = max(cur, len - cur - 1);
            d[scnt].push_back(fd[x]);
            dfs3(x, x);
            //cerr << x << " ";
            if(x == fat[x]) break;
            x = fat[x];
            cur++;
        }
        //cerr << endl;
        sort(d[scnt].begin(), d[scnt].end());
        //cerr << "Distant:";
       // for(int dd : d[scnt]) cerr << dd << " ";
        //cerr << endl;
    }
    //cerr << endl;
    for(int _t = 1;_t <= q;_t++){
        int u, v;cin >> u >> v;
        if(col[u] == col[v]){
            ans[_t] = -1;
            continue;
        }
        u = col[u], v = col[v];
        //cerr << "Qrys" << _t << ":"; 
        if(d[u].size() < d[v].size()) swap(u, v);
        //cerr << u << " " << v << endl;
        qs[u].push_back({v, _t});
    }
    for(int u = 1;u <= scnt;u++){
        for(Qrys qq : qs[u]){
            int v = qq.v, id = qq.id;
            //cerr << id << ":" << u << " " << v << endl;
            if(rs[u].count(v)) ans[id] = rs[u][v];
            else{
                ans[id] = calc(u, v);
                rs[u][v] = ans[id];
            }
        }
    }
    for(int i = 1;i <= q;i++) cout << ans[i] << endl;
    return 0;
}