#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")


// T: monoid representing information of an interval.
//   T()  should return the identity.
//   T(S s)  should represent a single element of the array.
//   T::pull(const T &l, const T &r)  should pull two intervals.
template <class T> struct SegmentTreePoint {
  int logN, n;
  vector<T> ts;
  SegmentTreePoint() : logN(0), n(0) {}
  explicit SegmentTreePoint(int n_) {
    for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {}
    ts.resize(n << 1);
  }
  template <class S> explicit SegmentTreePoint(const vector<S> &ss) {
    const int n_ = ss.size();
    for (logN = 0, n = 1; n < n_; ++logN, n <<= 1) {}
    ts.resize(n << 1);
    for (int i = 0; i < n_; ++i) at(i) = T(ss[i]);
    build();
  }
  T &at(int i) {
    return ts[n + i];
  }
  void build() {
    for (int u = n; --u; ) pull(u);
  }

  inline void pull(int u) {
    ts[u].pull(ts[u << 1], ts[u << 1 | 1]);
  }

  // Changes the value of point a to s.
  template <class S> void change(int a, const S &s) {
    assert(0 <= a); assert(a < n);
    ts[a += n] = T(s);
    for (; a >>= 1; ) pull(a);
  }

  // Applies T::f(args...) to point a.
  template <class F, class... Args>
  void ch(int a, F f, Args &&... args) {
    assert(0 <= a); assert(a < n);
    (ts[a += n].*f)(args...);
    for (; a >>= 1; ) pull(a);
  }

  // Calculates the product for [a, b).
  T get(int a, int b) {
    assert(0 <= a); assert(a <= b); assert(b <= n);
    if (a == b) return T();
    T prodL, prodR, t;
    for (a += n, b += n; a < b; a >>= 1, b >>= 1) {
      if (a & 1) { t.pull(prodL, ts[a++]); prodL = t; }
      if (b & 1) { t.pull(ts[--b], prodR); prodR = t; }
    }
    t.pull(prodL, prodR);
    return t;
  }

  // Calculates T::f(args...) of a monoid type for [a, b).
  //   op(-, -)  should calculate the product.
  //   e()  should return the identity.
  template <class Op, class E, class F, class... Args>
#if __cplusplus >= 201402L
  auto
#else
  decltype((std::declval<T>().*F())())
#endif
  get(int a, int b, Op op, E e, F f, Args &&... args) {
    assert(0 <= a); assert(a <= b); assert(b <= n);
    if (a == b) return e();
    auto prodL = e(), prodR = e();
    for (a += n, b += n; a < b; a >>= 1, b >>= 1) {
      if (a & 1) prodL = op(prodL, (ts[a++].*f)(args...));
      if (b & 1) prodR = op((ts[--b].*f)(args...), prodR);
    }
    return op(prodL, prodR);
  }

  // Find min b s.t. T::f(args...) returns true,
  // when called for the partition of [a, b) from left to right.
  //   Returns n + 1 if there is no such b.
  template <class F, class... Args>
  int findRight(int a, F f, Args &&... args) {
    assert(0 <= a); assert(a <= n);
    if ((T().*f)(args...)) return a;
    if (a == n) return n + 1;
    a += n;
    for (; ; a >>= 1) if (a & 1) {
      if ((ts[a].*f)(args...)) {
        for (; a < n; ) {
          if (!(ts[a <<= 1].*f)(args...)) ++a;
        }
        return a - n + 1;
      }
      ++a;
      if (!(a & (a - 1))) return n + 1;
    }
  }

  // Find max a s.t. T::f(args...) returns true,
  // when called for the partition of [a, b) from right to left.
  //   Returns -1 if there is no such a.
  template <class F, class... Args>
  int findLeft(int b, F f, Args &&... args) {
    assert(0 <= b); assert(b <= n);
    if ((T().*f)(args...)) return b;
    if (b == 0) return -1;
    b += n;
    for (; ; b >>= 1) if ((b & 1) || b == 2) {
      if ((ts[b - 1].*f)(args...)) {
        for (; b <= n; ) {
          if (!(ts[(b <<= 1) - 1].*f)(args...)) --b;
        }
        return b - n - 1;
      }
      --b;
      if (!(b & (b - 1))) return -1;
    }
  }
};  // SegmentTreePoint<T>

////////////////////////////////////////////////////////////////////////////////

/*
  ans = max[S] min[w: L[i]<=w[i]<=R[i]] (\sum[i\in S] w[i] V[i]) / (w[0] + \sum[i\in S] w[i])
  
  ans >= t  possible?
  \forall w,  \sum[i\in S] w[i] (V[i] - t) >= w[0] t
  consider only:
    w[0] = R[0]
    w[i] = L[i]
    S = {i | V[i] >= t}
  
  \sum L[i] V[i] >= (R[0] + \sum[i] L[i]) t
  
  0/0 case: max V[i] s.t. L[i] > 0
*/

constexpr Int INF = 1001001001001001001LL;

struct Node {
  Int sumLV, sumL, minV;
  Node() : sumLV(0), sumL(0), minV(INF) {}
  Node(Int v, Int l) : sumLV(l * v), sumL(l), minV(v) {}
  void pull(const Node &l, const Node &r) {
    sumLV = l.sumLV + r.sumLV;
    sumL = l.sumL + r.sumL;
    minV = min(l.minV, r.minV);
  }
  bool testEasy() const {
    return (sumL > 0);
  }
  bool testHard(Int &lv, Int &l, Int &t) const {
    const Int lvlv = lv + sumLV;
    const Int ll = l + sumL;
    const Int tt = min(t, minV);
    if (tt < INF && lvlv >= ll * tt) return true;
    lv = lvlv;
    l = ll;
    t = tt;
    return false;
  }
};

int N, Q;
vector<Int> V;
vector<Int> L;
Int R;
vector<int> O;
vector<int> X;
vector<Int> LL, RR, VV;

SegmentTreePoint<Node> seg;

void solve() {
// cerr<<"[solve] V = "<<V<<", L = "<<L<<", R = "<<R<<endl;
  Int p = 0, q = 1;
  if (R == 0) {
    const int pos = seg.findLeft(seg.n, &Node::testEasy);
    if (pos >= 0) {
      p = seg.at(pos).minV;
      q = 1;
    }
  } else {
    Int lv = 0, l = R, t = INF;
    const int pos = seg.findLeft(seg.n, &Node::testHard, lv, l, t);
// cerr<<"  pos = "<<pos<<", lv = "<<lv<<", l = "<<l<<", t = "<<t<<endl;
    p = lv;
    q = l;
  }
  const Int g = __gcd(p, q);
  p /= g;
  q /= g;
  printf("%lld/%lld\n", p, q);
}

int main() {
  for (; ~scanf("%d%d", &N, &Q); ) {
    V.resize(N);
    for (int i = 0; i < N; ++i) scanf("%lld", &V[i]);
    L.resize(N);
    scanf("%*lld");
    for (int i = 0; i < N; ++i) scanf("%lld", &L[i]);
    scanf("%lld", &R);
    for (int i = 0; i < N; ++i) scanf("%*lld");
    O.assign(Q, 0);
    X.assign(Q, -2);
    LL.assign(Q, 0);
    RR.assign(Q, 0);
    VV.assign(Q, 0);
    for (int q = 0; q < Q; ++q) {
      scanf("%d%d", &O[q], &X[q]);
      --X[q];
      if (O[q] == 1) {
        scanf("%lld%lld", &LL[q], &RR[q]);
      } else if (O[q] == 2) {
        scanf("%lld", &VV[q]);
      } else {
        assert(false);
      }
    }
    
    vector<pair<Int, int>> ps;
    for (int i = 0; i < N; ++i) ps.emplace_back(V[i], i);
    for (int q = 0; q < Q; ++q) if (O[q] == 2) ps.emplace_back(VV[q], N + q);
    sort(ps.begin(), ps.end());
    const int psLen = ps.size();
// cerr<<"ps = "<<ps<<endl;
    
    vector<int> poss(N);
    seg = SegmentTreePoint<Node>(psLen);
    for (int i = 0; i < N; ++i) {
      poss[i] = lower_bound(ps.begin(), ps.end(), make_pair(V[i], i)) - ps.begin();
      seg.at(poss[i]) = Node(V[i], L[i]);
    }
    seg.build();
    
    solve();
    for (int q = 0; q < Q; ++q) {
      const int i = X[q];
      if (O[q] == 1) {
        if (~i) {
          L[i] = LL[q];
          seg.change(poss[i], Node(V[i], L[i]));
        } else {
          R = RR[q];
        }
      } else if (O[q] == 2) {
        seg.change(poss[i], Node());
        poss[i] = lower_bound(ps.begin(), ps.end(), make_pair(VV[q], N + q)) - ps.begin();
        V[i] = VV[q];
        seg.change(poss[i], Node(V[i], L[i]));
      } else {
        assert(false);
      }
      solve();
    }
  }
  return 0;
}