#include <bits/stdc++.h>
//#define int long long
//#define pb push_back
using namespace std;

typedef pair<int,int> pii;
typedef tuple<int,int,int> tp;
const int N = 6e5 + 5;
const int oo = 2e8;

char Q[N];
int U[N], V[N];

int n, mx, k, m, q, gc[N], gx[N], f[N], c[N], x[N], sum, s[N], R[N], g[N], TX, t[N], NG;
vector<tp> p[N];

int st[5][N << 2], lz[5][N << 2];

void dolz(int j,int i){
    if(lz[j][i] == 0) return;
    int x = lz[j][i];
    lz[j][i] = 0;
    lz[j][i << 1] += x;
    lz[j][i << 1|1] += x;
    st[j][i << 1] += x;
    st[j][i << 1|1] += x;
}

void update(int j,int i,int l,int r,int u,int v,int x){
    if(l > r || l > v || r < u) return;
    if(u <= l && r <= v) {
        st[j][i] += x;
        lz[j][i] += x;
        return;
    }
    dolz(j, i);
    int mid = (l + r) >> 1;
    update(j, i << 1, l, mid, u, v, x);
    update(j, i << 1|1, mid + 1, r, u, v, x);
}

int get(int j,int i,int l,int r,int u){
    if(l > r || l > u || r < u || u == 0 || u == n) return 0;
    if(l == r) return st[j][i];
    dolz(j, i);
    int mid = (l + r) >> 1;
    return get(j, i << 1, l, mid, u) + get(j, i << 1|1, mid + 1, r, u);
}

int C(int u,int v){
    if(u == v) return 0;
    if(u > v) swap(u, v);
    int L1 = (get(0, 1, 1, mx, v - 1) - get(0, 1, 1, mx, u - 1) != 0 ? oo : s[v] - s[u]);
    int L2 = (g[n] || NG - (get(0, 1, 1, mx, v - 1) - get(0, 1, 1, mx, u - 1)) != 0 ? oo : sum - (s[v] - s[u]));
//    cout << u << " " << v << " " << L1 << " " << L2 << " " << get(0, 1, 1, mx, u - 1) << " r\n";
    return min(L1, L2);
}

int X(int u,int v){
    if(u == v) return 0;
    if(R[u] > R[v]) swap(u, v);
    if(u == 1 && v == k){
        if(gx[0] || gx[m]) return oo;
        if(get(1, 1, 1, mx, n + m - 1) - get(1, 1, 1, mx, n) != 0) return oo;
        return TX;
    }
    if(u == 1){
        if(get(1, 1, 1, mx, v - 1) - get(1, 1, 1, mx, n) != 0 || gx[0] == true) return oo;
        return t[v] - t[u];
    }
    if(v == k){
        if(get(1, 1, 1, mx, n + m - 1) - get(1, 1, 1, mx, u - 1) != 0 || gx[m] == true) return oo;
        return t[v] - t[u];
    }
    if(get(1, 1, 1, mx, v - 1) - get(1, 1, 1, mx, u - 1) != 0) return oo;
    return t[v] - t[u];
}

void sub3(){

    mx = n + m;

    for(int i = 2; i <= n; i ++) s[i] = s[i - 1] + c[i - 1];

    R[1] = 0;
    int cnt = 0;
    for(int i = n + 1; i <= n + m; i ++){
        g[i] = 1;
        R[i] = ++cnt;
        t[i] = t[i - 1] + x[i - n - 1];
    }
    R[k] = ++cnt;
    t[k] = t[n + m] + x[m];

    for(int j = 1; j <= q; j ++){
        char type = Q[j];
        if(type == 'q'){
            int u = U[j], v = V[j];
            int kq = oo;
            if(g[u] == g[v]){
                if(g[u] == 1){
                    kq = min({X(u, v), X(u, 1) + X(v, k) + C(1, k), C(1, k) + X(u, k) + X(v, 1)});
                }else{
                    kq = min({C(u, v), C(1, u) + C(k, v) + X(1, k), C(k, u) + C(1, v) + X(1, k)});
                }
            }else{
                if(g[u] == 1){
                    kq = min({X(1, u) + C(1, v), X(k, u) + C(k, v)}) ;
                }else{
                    kq = min({X(k, v) + C(k, u), X(1, v) + C(1, u)});
                }
            }
            if(kq >= oo) cout << "impossible\n";
            else cout << kq << "\n";
        }else if(type == 'c'){
            int i = U[j];
            if(gc[i] == 0){
                NG++;
                update(0, 1, 1, mx, i, n, 1);
                gc[i] = 1;
            }else{
                NG--;
                gc[i] = 0;
                update(0, 1, 1, mx, i, n, -1);
            }
        }else{
            int i = U[j];
            if(gx[i] == 0){
                if(i != 0 && i != m) update(1, 1, 1, mx, n + i, n + m, 1);
                gx[i] = 1;
            }else{
                gx[i] = 0;
                if(i != 0 && i != m) update(1, 1, 1, mx, n + i, n + m, -1);
            }
        }
    }
}

int dij(int u,int v){
    for(int i = 1; i <= n + m; i ++) f[i] = oo;
    priority_queue<pii,vector<pii>,greater<pii>> pq;
    pq.push({f[u] = 0, u});
    while(!pq.empty()){
        int w, u; tie(w, u) = pq.top();
        pq.pop();
        if(w > f[u]) continue;
        for(auto tt : p[u]){
            int j, v, e; tie(j, v, e) = tt;
            if(e == 0){
                if(gc[v] == 1) continue;
                if(f[j] > w + c[v]) pq.push({f[j] = w + c[v], j});
            }else{
                if(gx[v] == 1) continue;
                if(f[j] > w + x[v]) pq.push({f[j] = w + x[v], j});
            }
        }
    }
    if(f[v] == oo) return -1;
    else return f[v];
}

void sub1(){
    while(q--){
        char type; cin >> type;
        if(type == 'q'){
            int u, v; cin >> u >> v;
            int what = dij(u, v);
            if(what == -1) cout << "impossible\n";
            else cout << what << "\n";
        }else if(type == 'c'){
            int i; cin >> i;
            gc[i] = 1 - gc[i];
        }else{
            int i; cin >> i;
            gx[i] = 1 - gx[i];
        }
    }
}

int calc(int u,int v){
    if(u == v) return 0;
    if(u > v) swap(u, v);
    return min(s[v] - s[u], sum - (s[v] - s[u]));
}

int calx(int u,int v){
    if(u == v) return 0;
    if(R[u] > R[v]) swap(u, v);
    return t[v] - t[u];
}

void sub2(){

    for(int i = 2; i <= n; i ++) s[i] = s[i - 1] + c[i - 1];

    R[1] = 0;
    int cnt = 0;
    for(int i = n + 1; i <= n + m; i ++){
        g[i] = 1;
        R[i] = ++cnt;
        t[i] = t[i - 1] + x[i - n - 1];
    }
    R[k] = ++cnt;
    t[k] = t[n + m] + x[m];

   for(int i = 1; i <= q; i ++){

        char type = Q[i];
        int u = U[i], v = V[i];
        if(g[u] == g[v]){
            if(g[u] == 1){
                cout << min({calx(u, v), calx(u, 1) + calx(v, k) + calc(1, k), calc(1, k) + calx(u, k) + calx(v, 1)}) << "\n";
            }else{
                cout << min({calc(u, v), calc(1, u) + calc(k, v) + TX, calc(k, u) + calc(1, v) + TX}) << "\n";
            }
        }else{
            if(g[u] == 1){
                cout << min({calx(1, u) + calc(1, v), calx(k, u) + calc(k, v)}) << "\n";
            }else{
                cout << min({calx(k, v) + calc(k, u), calx(1, v) + calc(1, u)}) << "\n";
            }
        }
    }
}


signed main(){
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    if(fopen("train.inp","r")){
        freopen("train.inp","r",stdin);
        freopen("train.out","w",stdout);
    }
    cin >> n >> k >> m >> q;
    for(int i = 1; i <= n; i ++){
        cin >> c[i];
        sum += c[i];
        #define pb push_back
        p[i].push_back({i % n + 1, i, 0});
        p[i % n + 1].pb({i, i, 0});
    }
    for(int i = 0; i <= m; i ++){
        cin >> x[i];
        TX += x[i];
        if(i == 0){
            p[1].pb({n + 1, i, 1});
            p[n + 1].pb({1, i, 1});
        }
        else if(i == m){
            p[n + m].pb({k, i, 1});
            p[k].pb({n + m, i, 1});
        }
        else{
            p[n + i].pb({n + i + 1, i, 1});
            p[n + i + 1].pb({n + i, i, 1});
        }
    }
//    if(n <= 2000 && q <= 2000 && k <= 2000 && m <= 2000){
//        sub1();
//        return 0;
//    }
    bool ff = true;
    for(int i = 1; i <= q; i ++){
        cin >> Q[i];
        if(Q[i] == 'q') cin >> U[i] >> V[i];
        else{
            ff = false;
            cin >> U[i];
        }
    }
    if(ff) sub2();
    else sub3();
}