#include<bits/stdc++.h>
#pragma GCC optimize(2)
#define mod 1000000007LL
using namespace std;

struct frac{
	long long z, m;
	
	friend frac operator + (const frac &a, const frac &b){
		long long tmp = __gcd(a.m, b.m);
		frac res;
		res.m = a.m / tmp * b.m;
		res.z = (b.m / tmp * a.z) + (a.m / tmp * b.z);
		tmp = __gcd(res.m, res.z);
		res.m /= tmp, res.z /= tmp;
		return res;
	}
	
	friend frac operator * (const frac &a, const frac &b){
		frac res;
		res.m = a.m * b.m;
		res.z = a.z * b.z;
		long long tmp = __gcd(res.m, res.z);
		res.m /= tmp, res.z /= tmp;
		return res;
	}
	
	friend frac operator * (const frac &a, const int &b){
		frac res;
		res.m = a.m;
		res.z = a.z * b;
		long long tmp = __gcd(res.m, res.z);
		res.m /= tmp, res.z /= tmp;
		return res;
	}
};

int N, M, Q, ty, cid = 0;
int u, v;
int pos1, pos2, maxn;
vector<int> E[100005];
int F[100005];
bool vis[2][100005];
int dis[2][100005];
int in[100005], siz[100005];
frac val[100005];
set<int> st;

int find(int x){
	if (F[x] == x) return F[x];
	F[x] = find(F[x]);
	return F[x];
}

void merge(int x, int y){
	int fx = find(x), fy = find(y);
	if (fx == fy) return;
	F[fx] = fy;
}

void dfs(int u, int typ, int cid){
	// cout << u << " " << dis[typ][u] << " " << cid << ";;\n";
	st.insert(u);
	in[u] = cid;
	if (typ == 0 && dis[0][u] > maxn){
		maxn = dis[0][u];
		pos2 = u;
	}
	for (auto && v : E[u]){
		if (vis[typ][v]) continue;
		vis[typ][v] = 1;
		dis[typ][v] = min(dis[typ][v], dis[typ][u] + 1);
		dfs(v, typ, cid);
	}
}

long long qpow(long long a, long long b){
	long long res = 1;
	while (b){
		if (b & 1) res = (res * a) % mod;
		a = (a * a) % mod;
		b >>= 1;
	}
	return res;
}

int main(){
#ifndef ONLINE_JUDGE
	freopen("../data.in", "r", stdin);
	freopen("../data.out", "w", stdout);
#endif

	scanf("%d %d %d %d", &N, &M, &Q, &ty);
	for (int i = 1; i <= N; i ++) F[i] = i;
	while (M --){
		scanf("%d %d", &u, &v);
		E[u].push_back(v);
		E[v].push_back(u);
		merge(u, v);
	}
	memset(dis, 0x3f, sizeof(dis));
	for (int i = 1; i <= N; i ++){
		val[i].m = 1;
	}
	for (int i = 1; i <= N; i ++){
		if (vis[0][i]) continue;
		pos1 = i, maxn = -1;
		vis[0][pos1] = 1, dis[0][pos1] = 0;
		dfs(pos1, 0, ++ cid);
		pos1 = pos2, maxn = -1;
		for (auto && i : st){
			vis[0][i] = 0, dis[0][i] = 0x3f3f3f3f;
		}
		vis[0][pos1] = 1, dis[0][pos1] = 0;
		dfs(pos1, 0, cid);
		// cout << pos1 << "------" << pos2 << ";;\n";
		siz[cid] = st.size();
		vis[1][pos2] = 1, dis[1][pos2] = 0;
		dfs(pos2, 1, cid);
		for (auto && i : st){
			val[cid] = val[cid] + (frac){1LL, siz[cid]} * max(dis[0][i], dis[1][i]);
			// cout << i << "[]" << max(dis[0][i], dis[1][i]) << ";;\n";
		}
		st.clear();
	}
	while (Q --){
		scanf("%d %d", &u, &v);
		if (find(u) == find(v)){
			printf("-1\n");
			continue;
		}
		frac ans = val[in[u]] + val[in[v]] + (frac){1, 1};
		// printf("%lld %lld\n", ans.z, ans.m);
		printf("%lld\n", (qpow(ans.m, mod - 2) * ans.z) % mod);
	}

	return 0;
}