#include <bits/stdc++.h>
#define MOD 1000000007
#define int long long
using namespace std;
int read()
{
    int x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9')
    {
        if (ch == '-')
            f = -1;
        ch = getchar();
    }
    while (ch >= '0' && ch <= '9')
    {
        x = (x << 1) + (x << 3) + ch - '0';
        ch = getchar();
    }
    return x * f;
}
int n, m, q, u, v, st, f[200001], siz[200001], my, res, ress, xx, yy, jc[200001], inv[200001], maxn[200001], deep[200001], ans[200001];
vector<int> e[200001], fa[200001], cnt[200001], sum[200001];
map<pair<int, int>, int> vis;
int find(int x)
{
    if (x == f[x])
        return x;
    return f[x] = find(f[x]);
}
void merge(int x, int y)
{
    int fx = find(x), fy = find(y);
    if (fx != fy)
    {
        f[fx] = fy;
        siz[fy] += siz[fx];
    }
}
void dfs(int u, int dep, int f = -1)
{
    maxn[u] = max(maxn[u], dep);
    deep[u] = dep;
    for (auto v : e[u])
    {
        if (v != f)
        {
            dfs(v, dep + 1, u);
        }
    }
}
void exgcd(int a, int b)
{
    if (b == 0)
    {
        xx = 1;
        yy = 0;
        return;
    }
    exgcd(b, a % b);
    int t = xx;
    xx = yy;
    yy = t - a / b * yy;
}
int qpow(int a, int b)
{
    int res = 1;
    while (b)
    {
        if (b & 1)
            res = res * a % MOD;
        a = a * a % MOD;
        b >>= 1;
    }
    return res;
}
void init()
{
    inv[0] = 1;
    jc[0] = 1;
    for (int i = 1; i <= 200000; i++)
    {
        jc[i] = jc[i - 1] * i % MOD;
        siz[i] = 1;
        f[i] = i;
        inv[i] = qpow(jc[i], MOD - 2);
    }
}
int work(int x, int y)
{
    int nowmax = max(ans[x], ans[y]), res1 = siz[x] * siz[y], res2 = 0;
    for (auto i : fa[x])
    {
        if (nowmax - maxn[i] <= siz[y])
        {
            if (nowmax - maxn[i])
            {
                int a = cnt[y][siz[y]] - cnt[y][nowmax - maxn[i] - 1];
                int b = sum[y][siz[y]] - sum[y][nowmax - maxn[i] - 1];
                res1 -= a;
                res2 += b + a * maxn[i];
            }
            else
            {
                res1 -= cnt[y][siz[y]];
                res2 += sum[y][siz[y]];
                res2 += maxn[i] * cnt[y][siz[y]];
            }
        }
    }
    res = res1 * nowmax + res2;
    ress = siz[x] * siz[y];
    exgcd(ress, MOD);
    xx = (xx % MOD + MOD) % MOD;
    // cout << res << ' ' << siz[x] << ' ' << siz[y] << ' ' << inv[siz[x]] << ' ' << inv[siz[y]] << endl;
    return res * xx % MOD;
}
signed main()
{
    n = read();
    m = read();
    q = read();
    my = read();
    init();
    for (int i = 1; i <= m; i++)
    {
        u = read();
        v = read();
        e[u].push_back(v);
        e[v].push_back(u);
        merge(u, v);
    }
    for (int i = 1; i <= n; i++)
    {
        fa[find(i)].push_back(i);
    }
    for (int i = 1; i <= n; i++)
    {
        if (f[i] == i)
        {
            st = 0;
            dfs(i, 0);
            for (auto j : fa[i])
            {
                if (deep[j] > deep[st])
                {
                    st = j;
                }
            }
            dfs(st, 0);
            for (auto j : fa[i])
            {
                if (deep[j] > deep[st])
                {
                    st = j;
                }
            }
            dfs(st, 0);
            sum[i].resize(siz[i] + 3);
            cnt[i].resize(siz[i] + 3);
            for (auto j : fa[i])
            {
                cnt[i][maxn[j]]++;
                sum[i][maxn[j]] = sum[i][maxn[j]] + maxn[j] + 1;
                ans[i] = max(ans[i], maxn[j]);
            }
            for (int j = 1; j <= siz[i]; j++)
            {
                cnt[i][j] += cnt[i][j - 1];
                sum[i][j] += sum[i][j - 1];
            }
        }
    }
    while (q--)
    {
        u = read();
        v = read();
        u = find(u);
        v = find(v);
        if (u == v)
        {
            printf("-1\n");
            continue;
        }
        if (siz[u] > siz[v])
        {
            swap(u, v);
        }
        if (vis[{u, v}])
        {
            printf("%lld\n", vis[{u, v}]);
        }
        else
        {
            vis[{u, v}] = work(u, v);
            printf("%lld\n", vis[{u, v}]);
        }
    }
    return 0;
}