#include <bits/stdc++.h>
using namespace std;
typedef long long i64; 

const int N = 2e5 + 5, W = 1e6; 

int n, m;
int V[N], L[N], R[N]; 

i64 Tw[W * 4 + 50], Twv[W * 4 + 50];
void update(int o, int l, int r, int p, int x, i64 y) { 
    if (l == r) return Tw[o] += x, Twv[o] += y, void(); 
    int mid = l + r >> 1; 
    if (p <= mid) update(o << 1, l, mid, p, x, y); 
    else update(o << 1 | 1, mid + 1, r, p, x, y); 
    Tw[o] = Tw[o << 1] + Tw[o << 1 | 1];
    Twv[o] = Twv[o << 1] + Twv[o << 1 | 1];
}

i64 Aw, Awv, pos; 
void query(int o, int l, int r, i64 sw, i64 swv) {
    if (l == r) return pos = l, Aw = sw, Awv = swv, void(); 
    int mid = l + r >> 1; 
    i64 nsw = sw + Tw[o << 1 | 1], nswv = swv + Twv[o << 1 | 1]; 
    if (Tw[o << 1 | 1] && nswv - (mid + 1) * nsw >= (mid + 1ll) * R[0]) query(o << 1 | 1, mid + 1, r, sw, swv); 
    else query(o << 1, l, mid, nsw, nswv); 
}

void solve(void) {
    query(1, 0, W, 0, 0);
    Aw += R[0]; 
    if (Aw == 0) return cout << pos << "/1\n", void(); 
    i64 g = __gcd(Aw, Awv); 
    Aw /= g, Awv /= g; 
    cout << Awv << "/" << Aw << "\n"; 
}

int main(void) {
    // ios::sync_with_stdio(0); 
    cin >> n >> m;
    for (int i = 1; i <= n; ++i) cin >> V[i]; 
    for (int i = 0; i <= n; ++i) cin >> L[i]; 
    for (int i = 0; i <= n; ++i) cin >> R[i]; 

    for (int i = 1; i <= n; ++i) update(1, 0, W, V[i], L[i], 1ll * L[i] * V[i]); 
    solve(); 

    while (m--) {
        int op, x, y, z; cin >> op >> x >> y; 
        update(1, 0, W, V[x], -L[x], -L[x] * V[x]);
        if (op == 1) cin >> z, L[x] = y, R[x] = z; 
        else V[x] = y; 
        update(1, 0, W, V[x], L[x], 1ll * L[x] * V[x]); 
        solve();
    }
    return 0; 
}