#line 1 "a.cpp"

#include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <vector>
#include <list>
#include <queue>
#include <stack>
#include <deque>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>
#include <numeric>
#include <cmath>
#include <climits>
#include <cassert>
#include <functional>
#include <iterator>
#include <utility>
#include <complex>
#include <bitset>
#include <chrono>
#include <random>
#include <limits>
#include <optional>
#include <variant>
#include <any>

#include <array>
#include <bit>
#include <compare>
#include <concepts>
#include <format>
#include <numbers>
#include <ranges>
#include <span>
#include <string_view>
#include <tuple>
#include <type_traits>
#include <version>
using namespace std;
using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = numeric_limits<double>::infinity();
template <>
constexpr long double infty<long double> =
    numeric_limits<long double>::infinity();

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using pq_max = priority_queue<T>;
template <class T>
using pq_min = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a) - 1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a) - 1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b) - 1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define all(x) (x).begin(), (x).end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T kth_bit(int k) {
  return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
  return x >> k & 1;
}

template <typename UINT>
struct all_bit {
  struct iter {
    UINT s;
    iter(UINT s) : s(s) {}
    int operator*() const { return lowbit(s); }
    iter &operator++() {
      s &= s - 1;
      return *this;
    }
    bool operator!=(const iter) const { return s != 0; }
  };
  UINT s;
  all_bit(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

template <typename UINT>
struct all_subset {
  static_assert(is_unsigned<UINT>::value);
  struct iter {
    UINT s, t;
    bool ed;
    iter(UINT s) : s(s), t(s), ed(0) {}
    UINT operator*() const { return s ^ t; }
    iter &operator++() {
      (t == 0 ? ed = 1 : t = (t - 1) & s);
      return *this;
    }
    bool operator!=(const iter) const { return !ed; }
  };
  UINT s;
  all_subset(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

constexpr ll TEN[] = {
    1LL,
    10LL,
    100LL,
    1000LL,
    10000LL,
    100000LL,
    1000000LL,
    10000000LL,
    100000000LL,
    1000000000LL,
    10000000000LL,
    100000000000LL,
    1000000000000LL,
    10000000000000LL,
    100000000000000LL,
    1000000000000000LL,
    10000000000000000LL,
    100000000000000000LL,
    1000000000000000000LL,
};

template <typename T, typename U>
T SUM(const U &A) {
  return std::accumulate(A.begin(), A.end(), T{});
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
template <class C, class T>
inline long long LB(const C &c, const T &x) {
  return lower_bound(c.begin(), c.end(), x) - c.begin();
}
template <class C, class T>
inline long long UB(const C &c, const T &x) {
  return upper_bound(c.begin(), c.end(), x) - c.begin();
}
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <class T, class Container, class Compare>
T POP(priority_queue<T, Container, Compare> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (llabs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  T c = max<T>(a, b);
  bool changed = (c != a);
  a = c;
  return changed;
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  T c = min<T>(a, b);
  bool changed = (c != a);
  a = c;
  return changed;
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vc<T> cumsum(const vc<U> &A, int off = 1) {
  int N = A.size();
  vc<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vc<int> argsort(const vc<T> &A) {
  vc<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}

template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &...others) {
  vc<T> &res = first;
  (res.insert(res.end(), others.begin(), others.end()), ...);
}

#line 1 "ds/node_pool.hpp"
// マルチテストケースに弱いので static で確保すること
template <class Node>
struct Node_Pool {
  struct Slot {
    union alignas(Node) {
      Slot* next;
      unsigned char storage[sizeof(Node)];
    };
  };
  using np = Node*;

  static constexpr int CHUNK_SIZE = 1 << 12;

  vc<unique_ptr<Slot[]>> chunks;
  Slot* cur = nullptr;
  int cur_used = 0;
  Slot* free_head = nullptr;

  Node_Pool() { alloc_chunk(); }

  template <class... Args>
  np create(Args&&... args) {
    Slot* s = new_slot();
    return ::new (s) Node(forward<Args>(args)...);
  }

  np clone(const np x) {
    assert(x);
    Slot* s = new_slot();
    return ::new (s) Node(*x);  // コピーコンストラクタ呼び出し
  }

  void destroy(np x) {
    if (!x) return;
    x->~Node();
    auto s = reinterpret_cast<Slot*>(x);
    s->next = free_head;
    free_head = s;
  }

  void reset() {
    free_head = nullptr;
    if (!chunks.empty()) {
      cur = chunks[0].get();
      cur_used = 0;
    }
  }

 private:
  void alloc_chunk() {
    chunks.emplace_back(make_unique<Slot[]>(CHUNK_SIZE));
    cur = chunks.back().get();
    cur_used = 0;
  }

  Slot* new_slot() {
    if (free_head) {
      Slot* s = free_head;
      free_head = free_head->next;
      return s;
    }
    if (cur_used == CHUNK_SIZE) alloc_chunk();
    return &cur[cur_used++];
  }
};
#line 3 "ds/splaytree/splaytree.hpp"

// Node 型を別に定義して使う
template <typename Node>
struct SplayTree {
  Node_Pool<Node> pool;
  using np = Node *;
  using X = typename Node::value_type;
  using A = typename Node::operator_type;

  void free_subtree(np c) {
    if (!c) return;
    auto dfs = [&](auto &dfs, np c) -> void {
      if (c->l) dfs(dfs, c->l);
      if (c->r) dfs(dfs, c->r);
      c->p = c->l = c->r = nullptr;
      pool.destroy(c);
    };
    dfs(dfs, c);
  }

  void reset() { pool.reset(); }

  np new_root() { return nullptr; }

  np new_node(const X &x) {
    np n = pool.create();
    Node::new_node(n, x);
    return n;
  }

  np new_node(const vc<X> &dat) {
    auto dfs = [&](auto &dfs, int l, int r) -> np {
      if (l == r) return nullptr;
      if (r == l + 1) return new_node(dat[l]);
      int m = (l + r) / 2;
      np l_root = dfs(dfs, l, m);
      np r_root = dfs(dfs, m + 1, r);
      np root = new_node(dat[m]);
      root->l = l_root, root->r = r_root;
      if (l_root) l_root->p = root;
      if (r_root) r_root->p = root;
      root->update();
      return root;
    };
    return dfs(dfs, 0, len(dat));
  }

  u32 get_size(np root) { return (root ? root->size : 0); }

  np merge(np l_root, np r_root) {
    if (!l_root) return r_root;
    if (!r_root) return l_root;
    assert((!l_root->p) && (!r_root->p));
    splay_kth(r_root, 0);  // splay したので push 済
    r_root->l = l_root;
    l_root->p = r_root;
    r_root->update();
    return r_root;
  }
  np merge3(np a, np b, np c) { return merge(merge(a, b), c); }
  np merge4(np a, np b, np c, np d) { return merge(merge(merge(a, b), c), d); }

  pair<np, np> split(np root, u32 k) {
    assert(!root || !root->p);
    if (k == 0) return {nullptr, root};
    if (k == (root->size)) return {root, nullptr};
    splay_kth(root, k - 1);
    np right = root->r;
    root->r = nullptr, right->p = nullptr;
    root->update();
    return {root, right};
  }
  tuple<np, np, np> split3(np root, u32 l, u32 r) {
    np nm, nr;
    tie(root, nr) = split(root, r);
    tie(root, nm) = split(root, l);
    return {root, nm, nr};
  }
  tuple<np, np, np, np> split4(np root, u32 i, u32 j, u32 k) {
    np d;
    tie(root, d) = split(root, k);
    auto [a, b, c] = split3(root, i, j);
    return {a, b, c, d};
  }

  tuple<np, np, np> split_L_root_R(np root) {
    u32 s = (root->l ? root->l->size : 0);
    return split3(root, s, s + 1);
  }

  // 部分木が区間 [l,r) に対応するようなノードを作って返す
  // そのノードが root になるわけではないので、
  // このノードを参照した後にすぐに splay して根に持ち上げること
  void goto_between(np &root, u32 l, u32 r) {
    if (l == 0 && r == root->size) return;
    if (l == 0) {
      splay_kth(root, r);
      root = root->l;
      return;
    }
    if (r == root->size) {
      splay_kth(root, l - 1);
      root = root->r;
      return;
    }
    splay_kth(root, r);
    np rp = root;
    root = rp->l;
    root->p = nullptr;
    splay_kth(root, l - 1);
    root->p = rp;
    rp->l = root;
    rp->update();
    root = root->r;
  }

  vc<X> get_all(const np &root) {
    vc<X> res;
    auto dfs = [&](auto &dfs, np root) -> void {
      if (!root) return;
      root->push();
      dfs(dfs, root->l);
      res.eb(root->get());
      dfs(dfs, root->r);
    };
    dfs(dfs, root);
    return res;
  }

  X get(np &root, u32 k) {
    assert(root == nullptr || !root->p);
    splay_kth(root, k);
    return root->get();
  }

  void set(np &root, u32 k, const X &x) {
    assert(root != nullptr && !root->p);
    splay_kth(root, k);
    root->set(x);
  }

  void multiply(np &root, u32 k, const X &x) {
    assert(root != nullptr && !root->p);
    splay_kth(root, k);
    root->multiply(x);
  }

  X prod(np &root, u32 l, u32 r) {
    assert(root == nullptr || !root->p);
    using Mono = typename Node::Monoid_X;
    if (l == r) return Mono::unit();
    assert(0 <= l && l < r && r <= root->size);
    goto_between(root, l, r);
    X res = root->prod;
    splay(root, true);
    return res;
  }

  X prod(np &root) {
    assert(root == nullptr || !root->p);
    using Mono = typename Node::Monoid_X;
    return (root ? root->prod : Mono::unit());
  }

  void apply(np &root, u32 l, u32 r, const A &a) {
    if (l == r) return;
    assert(0 <= l && l < r && r <= root->size);
    goto_between(root, l, r);
    root->apply(a);
    splay(root, true);
  }
  void apply(np &root, const A &a) {
    if (!root) return;
    root->apply(a);
  }

  void reverse(np &root, u32 l, u32 r) {
    assert(root == nullptr || !root->p);
    if (l == r) return;
    assert(0 <= l && l < r && r <= root->size);
    goto_between(root, l, r);
    root->reverse();
    splay(root, true);
  }
  void reverse(np root) {
    if (!root) return;
    root->reverse();
  }

  void rotate(Node *n) {
    // n を根に近づける。push, update は rotate の外で行う。
    Node *pp, *p, *c;
    p = n->p;
    pp = p->p;
    if (p->l == n) {
      c = n->r;
      n->r = p;
      p->l = c;
    } else {
      c = n->l;
      n->l = p;
      p->r = c;
    }
    if (pp && pp->l == p) pp->l = n;
    if (pp && pp->r == p) pp->r = n;
    n->p = pp;
    p->p = n;
    if (c) c->p = p;
  }

  void push_from_root(np c) {
    if (!c->p) {
      c->push();
      return;
    }
    push_from_root(c->p);
    c->push();
  }

  void splay(Node *me, bool push_from_root_done) {
    // これを呼ぶ時点で、me の祖先（me を除く）は既に push 済であることを仮定
    // 特に、splay 終了時点で me は upd / push 済である
    if (!push_from_root_done) push_from_root(me);
    me->push();
    while (me->p) {
      np p = me->p;
      np pp = p->p;
      if (!pp) {
        rotate(me);
        p->update();
        break;
      }
      bool same = (p->l == me && pp->l == p) || (p->r == me && pp->r == p);
      if (same) rotate(p), rotate(me);
      if (!same) rotate(me), rotate(me);
      pp->update(), p->update();
    }
    // me の update は最後だけでよい
    me->update();
  }

  void splay_kth(np &root, u32 k) {
    assert(0 <= k && k < (root->size));
    while (1) {
      root->push();
      u32 s1 = (root->l ? root->l->size : 0);
      u32 s2 = (root->size) - (root->r ? root->r->size : 0);
      if (k < s1) root = root->l;
      elif (k < s2) { break; }
      else {
        k -= s2;
        root = root->r;
      }
    }
    splay(root, true);
  }

  // check(x), 左側のノード全体が check を満たすように切る
  template <typename F>
  pair<np, np> split_max_right(np root, F check) {
    if (!root) return {nullptr, nullptr};
    assert(!root->p);
    np c = find_max_right(root, check);
    if (!c) {
      splay(root, true);
      return {nullptr, root};
    }
    splay(c, true);
    np right = c->r;
    if (!right) return {c, nullptr};
    right->p = nullptr;
    c->r = nullptr;
    c->update();
    return {c, right};
  }

  // check(x, cnt), 左側のノード全体が check を満たすように切る
  template <typename F>
  pair<np, np> split_max_right_cnt(np root, F check) {
    if (!root) return {nullptr, nullptr};
    assert(!root->p);
    np c = find_max_right_cnt(root, check);
    if (!c) {
      splay(root, true);
      return {nullptr, root};
    }
    splay(c, true);
    np right = c->r;
    if (!right) return {c, nullptr};
    right->p = nullptr;
    c->r = nullptr;
    c->update();
    return {c, right};
  }

  // 左側のノード全体の prod が check を満たすように切る
  template <typename F>
  pair<np, np> split_max_right_prod(np root, F check) {
    if (!root) return {nullptr, nullptr};
    assert(!root->p);
    np c = find_max_right_prod(root, check);
    if (!c) {
      splay(root, true);
      return {nullptr, root};
    }
    splay(c, true);
    np right = c->r;
    if (!right) return {c, nullptr};
    right->p = nullptr;
    c->r = nullptr;
    c->update();
    return {c, right};
  }

  template <typename F>
  np find_max_right(np root, const F &check) {
    // 最後に見つけた ok の点、最後に探索した点
    np last_ok = nullptr, last = nullptr;
    while (root) {
      last = root;
      root->push();
      if (check(root->x)) {
        last_ok = root;
        root = root->r;
      } else {
        root = root->l;
      }
    }
    splay(last, true);
    return last_ok;
  }

  template <typename F>
  np find_max_right_cnt(np root, const F &check) {
    // 最後に見つけた ok の点、最後に探索した点
    np last_ok = nullptr, last = nullptr;
    ll n = 0;
    while (root) {
      last = root;
      root->push();
      ll k = (root->size) - (root->r ? root->r->size : 0);
      if (check(root->x, n + k)) {
        last_ok = root;
        n += k;
        root = root->r;
      } else {
        root = root->l;
      }
    }
    splay(last, true);
    return last_ok;
  }

  template <typename F>
  np find_max_right_prod(np root, const F &check) {
    using Mono = typename Node::Monoid_X;
    X prod = Mono::unit();
    // 最後に見つけた ok の点、最後に探索した点
    np last_ok = nullptr, last = nullptr;
    while (root) {
      last = root;
      root->push();
      np tmp = root->r;
      root->r = nullptr;
      root->update();
      X lprod = Mono::op(prod, root->prod);
      root->r = tmp;
      root->update();
      if (check(lprod)) {
        prod = lprod;
        last_ok = root;
        root = root->r;
      } else {
        root = root->l;
      }
    }
    splay(last, true);
    return last_ok;
  }
};
#line 2 "alg/monoid/add_pair.hpp"

template <typename E>
struct Monoid_Add_Pair {
  using value_type = pair<E, E>;
  using X = value_type;
  static constexpr X op(const X &x, const X &y) {
    return {x.fi + y.fi, x.se + y.se};
  }
  static constexpr X inverse(const X &x) { return {-x.fi, -x.se}; }
  static constexpr X unit() { return {0, 0}; }
  static constexpr bool commute = true;
};
#line 3 "convex/slope_trick/slope_super.hpp"

namespace SLOPE_TRICK_SUPER {
/*
傾きと座標が全部 T.
(x0,y0,a0) / 傾き変化を splay tree で持つ.
末尾には必ず infty が入っているようにする.
(0,10),(1,6),(3,4),(6,7)
->
(x0,y0,a0)=(0,10,-4)
dat = ([1,3],[3,2])

f(x) の計算, (min,argmin) の計算
加法, 畳み込み

加法: easy
f(x) の計算: sum(a), sum(xa) が要る
畳み込み: x->x+c が要る
*/

template <typename T>
struct Node {
  using value_type = pair<T, T>;
  using operator_type = T;
  using np = Node *;
  using Monoid_X = Monoid_Add_Pair<T>;

  np p, l, r;
  bool rev;
  u32 size;
  pair<T, T> x;     // (x,a)
  pair<T, T> prod;  // (a sum, xa sum)
  T add_x;

  static void new_node(np n, const pair<T, T> &x) {
    n->p = n->l = n->r = nullptr, n->rev = 0, n->size = 1;
    n->x = x, n->prod = {x.se, x.fi * x.se}, n->add_x = 0;
  }

  void update() {
    size = 1;
    if (l) {
      size += l->size;
    }
    if (r) {
      size += r->size;
    }
    prod = {x.se, x.fi * x.se};
    if (l) prod = Monoid_X::op(prod, l->prod);
    if (r) prod = Monoid_X::op(prod, r->prod);
  }

  void push() {
    assert(!rev);
    if (add_x == 0) return;
    if (l)
      l->x.fi += add_x, l->prod.se += l->prod.fi * add_x, l->add_x += add_x;
    if (r)
      r->x.fi += add_x, r->prod.se += r->prod.fi * add_x, r->add_x += add_x;
    add_x = 0;
  }

  void apply(T a) { x.fi += a, prod.se += a * prod.fi, add_x += a; }

  // update, push 以外で呼ばれるものは、splay 後であることが想定されている。
  // したがってその時点で update, push 済であることを仮定してよい。
  pair<T, T> get() { return x; }
  void set(const pair<T, T> &xx) {
    x = xx;
    update();
  }
};

// 関数は破壊的な変更にされる
template <typename T>
struct Slope_Trick_Super {
  SplayTree<Node<T>> ST;
  using np = Node<T> *;

  struct FUNC {
    np root;  // 定義域がこわれていたら root == empty
    T x0, x1, a0, y0;
    int size() { return (root ? root->size : 0); }
  };

  // (L,R,a,b) : [L,R] で y=ax+b
  FUNC segment_func(T L, T R, T a, T b) {
    return {nullptr, L, R, a, a * L + b};
  }
  FUNC from_points(vc<pair<T, T>> &point) {
    return from_points(len(point),
                       [&](int i) -> pair<T, T> { return point[i]; });
  }
  template <typename F>
  FUNC from_points(int N, F f) {
    vc<T> X(N), Y(N);
    FOR(i, N) tie(X[i], Y[i]) = f(i);
    if (N == 1) return segment_func(X[0], X[0], 0, Y[0]);
    T a0 = (Y[1] - Y[0]) / (X[1] - X[0]);
    T x0 = X[0], x1 = X.back();
    vc<pair<T, T>> dat;
    T a = a0;
    FOR(i, 1, N - 1) {
      T a1 = (Y[i + 1] - Y[i]) / (X[i + 1] - X[i]);
      dat.eb(X[i], a1 - a), a = a1;
    }
    return FUNC{ST.new_node(dat), x0, x1, a0, Y[0]};
  }

  pair<T, T> domain(FUNC &f) { return {f.x0, f.x1}; }
  T eval(FUNC &f, T x) {
    auto [x0, x1] = domain(f);
    if (!(x0 <= x && x <= x1)) return infty<T>;
    auto [l, r] = ST.split_max_right(
        f.root, [&](auto dat) -> bool { return dat.fi <= x; });
    auto [a_sum, xa_sum] = ST.prod(l);
    f.root = ST.merge(l, r);
    return f.y0 + f.a0 * (x - x0) + a_sum * x - xa_sum;
  }
  FUNC restrict_domain(FUNC &f, T L, T R) {
    auto [x0, x1] = domain(f);
    chmax(L, x0), chmin(R, x1);
    if (L > R) {
      ST.free_subtree(f.root), f.root = nullptr;
      f.root = nullptr;
      f.x0 = infty<T>, f.x1 = -infty<T>;
      return f;
    }
    // まずは右側をちぢめる. R 以上の傾き変化を消してしまえばよい
    auto [l, r] = ST.split_max_right(
        f.root, [&](auto dat) -> bool { return dat.fi < R; });
    ST.free_subtree(r);
    // 左側をちぢめる.
    tie(l, r) =
        ST.split_max_right(l, [&](auto dat) -> bool { return dat.fi <= L; });
    auto [a_sum, xa_sum] = ST.prod(l);
    T new_a0 = f.a0 + a_sum;
    T new_y0 = f.y0 + f.a0 * (L - x0) + a_sum * L - xa_sum;
    ST.free_subtree(l);
    f.root = r, f.x0 = L, f.x1 = R, f.a0 = new_a0, f.y0 = new_y0;
    return f;
  }
  FUNC add(FUNC &f, FUNC &g) {
    T x0 = max(f.x0, g.x0);
    T x1 = min(f.x1, g.x1);
    restrict_domain(f, x0, x1), restrict_domain(g, x0, x1);
    if (x0 > x1) return f;
    T y0 = f.y0 + g.y0, a0 = f.a0 + g.a0;

    if (len(f) < len(g)) swap(f, g);
    auto tmp = ST.get_all(g.root);
    ST.free_subtree(g.root);
    f.x0 = x0, f.x1 = x1, f.a0 = a0, f.y0 = y0;
    if (!f.root) {
      f.root = ST.new_node(tmp);
      return f;
    }
    // あとは単に tmp を挿入していけばいい
    auto dfs = [&](auto &dfs, np root, int l, int r) -> void {
      if (l == r) return;
      root->push();
      T x = root->x.fi;
      // [l,m),[m,r)
      int m = binary_search([&](int i) -> bool { return tmp[i].fi >= x; }, r,
                            l - 1, 0);
      if (l < m) {
        if (!root->l) {
          root->l = ST.new_node({tmp.begin() + l, tmp.begin() + m});
        } else {
          dfs(dfs, root->l, l, m);
        }
        root->l->p = root;
      }
      if (m < r) {
        if (!root->r) {
          root->r = ST.new_node({tmp.begin() + m, tmp.begin() + r});
        } else {
          dfs(dfs, root->r, m, r);
        }
        root->r->p = root;
      }
      root->update();
    };
    dfs(dfs, f.root, 0, len(tmp));
    return f;
  }
  FUNC sum_all(vc<FUNC> &funcs) {
    assert(len(funcs) >= 1);
    T x0 = funcs[0].x0, x1 = funcs[0].x1;
    for (auto &g : funcs) chmax(x0, g.x0), chmin(x1, g.x1);
    if (x0 > x1) {
      for (auto &f : funcs) {
        ST.free_subtree(f.root);
      }
      return {nullptr, infty<T>, -infty<T>, 0, 0};
    }
    for (auto &f : funcs) f = restrict_domain(f, x0, x1);
    int idx = 0;
    FOR(i, 1, len(funcs)) if (len(funcs[idx]) < len(funcs[i])) idx = i;
    swap(funcs[idx], funcs.back());
    FUNC f = POP(funcs);
    vc<pair<T, T>> dat;
    for (auto &g : funcs) {
      f.y0 += g.y0, f.a0 += g.a0;
      auto tmp = ST.get_all(g.root);
      concat(dat, tmp);
      ST.free_subtree(g.root);
    }
    sort(all(dat));
    // あとは単に dat を挿入していけばいい
    if (!f.root) {
      f.root = ST.new_node(dat);
      return f;
    }
    auto dfs = [&](auto &dfs, np root, int l, int r) -> void {
      if (l == r) return;
      root->push();
      T x = root->x.fi;
      // [l,m),[m,r)
      int m = binary_search([&](int i) -> bool { return dat[i].fi >= x; }, r,
                            l - 1, 0);
      if (l < m) {
        if (!root->l) {
          root->l = ST.new_node({dat.begin() + l, dat.begin() + m});
        } else {
          dfs(dfs, root->l, l, m);
        }
        root->l->p = root;
      }
      if (m < r) {
        if (!root->r) {
          root->r = ST.new_node({dat.begin() + m, dat.begin() + r});
        } else {
          dfs(dfs, root->r, m, r);
        }
        root->r->p = root;
      }
      root->update();
    };
    dfs(dfs, f.root, 0, len(dat));
    return f;
  }

  FUNC shift(FUNC &f, T add_x, T add_y) {
    ST.apply(f.root, add_x);
    f.x0 += add_x, f.x1 += add_x, f.y0 += add_y;
    return f;
  }

  // h[z]=min(x+y==z)f(x)+g(y)
  FUNC convolve(FUNC &f, FUNC &g) {
    if (f.x0 > f.x1 || g.x0 > g.x1) {
      return {nullptr, infty<T>, -infty<T>, 0, 0};
    }
    if (len(f) < len(g)) swap(f, g);
    shift(f, g.x0, g.y0), shift(g, -g.x0, -g.y0);
    if (len(g) == 0) {
      return convolve_segment(f, 0, g.x1, g.a0, 0);
    }
    auto tmp = ST.get_all(g.root);
    ST.free_subtree(g.root);
    f = convolve_segment(f, 0, tmp[0].fi, g.a0, 0);
    T a = g.a0;
    FOR(i, len(tmp)) {
      T nx = (i + 1 < len(tmp) ? tmp[i + 1].fi : g.x1);
      a += tmp[i].se;
      f = convolve_segment(f, 0, nx - tmp[i].fi, a, 0);
      for (auto &[x, a] : ST.get_all(f.root)) {
        assert(f.x0 <= x && x <= f.x1);
        if (f.root) assert(!f.root->p);
      }
    }
    return f;
  }

  // [x0,x1], y=ax+b
  FUNC convolve_segment(FUNC &f, T x0, T x1, T a, T b) {
    assert(x0 <= x1);
    if (f.x0 > f.x1) {
      return {nullptr, infty<T>, -infty<T>, 0, 0};
    }
    f = shift(f, x0, a * x0 + b);
    T d = x1 - x0;
    if (d == 0) return f;
    // (0,0) から (x1,ax1) への線分をどこかに挿入する
    // 特に x0, y0 はこのままでよい
    if (f.x0 == f.x1) {
      return {nullptr, f.x0, f.x0 + d, a, f.y0};
    }
    // 先頭に挿入できる場合
    if (a <= f.a0) {
      ST.apply(f.root, d);
      f.root = ST.merge(ST.new_node({f.x0 + d, f.a0 - a}), f.root);
      f.x1 += d, f.a0 = a;
      return f;
    }
    // 末尾に挿入できる場合
    T a_last = f.a0 + ST.prod(f.root).fi;
    if (a_last <= a) {
      f.root = ST.merge(f.root, ST.new_node({f.x1, a - a_last}));
      f.x1 += d;
      return f;
    }
    // 間のどこかに挿入
    auto [l, r] = ST.split_max_right_prod(
        f.root, [&](auto prod) -> bool { return f.a0 + prod.fi < a; });
    T asum = ST.prod(l).fi;
    T a1 = a - (asum + f.a0);
    auto [xx, aa] = ST.get(r, 0);
    ST.apply(r, d);
    ST.set(r, 0, {xx + d, aa - a1});
    f.root = ST.merge3(l, ST.new_node({xx, a1}), r);
    f.x1 += d;
    return f;
  }

  FUNC add_const(FUNC &f, T a) {
    f.y0 += a;
    return f;
  }

  FUNC add_linear(FUNC &f, T a, T b) {
    f.y0 += a * f.x0 + b;
    f.a0 += a;
    return f;
  }

  // (a-x)+
  FUNC add_a_minus_x(FUNC &f, T a) {
    auto [x0, x1] = domain(f);
    if (x0 > x1) return f;
    if (a <= x0) return f;
    if (x1 <= a) return add_linear(f, -1, a);
    vc<pair<T, T>> point;
    point.eb(x0, a - x0), point.eb(a, 0), point.eb(x1, 0);
    FUNC g = from_points(point);
    return add(f, g);
  }

  // (x-a)+
  FUNC add_x_minus_a(FUNC &f, T a) {
    auto [x0, x1] = domain(f);
    if (x0 > x1) return f;
    if (a <= x0) return add_linear(f, 1, -a);
    if (x1 <= a) return f;
    vc<pair<T, T>> point;
    point.eb(x0, 0), point.eb(a, 0), point.eb(x1, x1 - a);
    FUNC g = from_points(point);
    return add(f, g);
  }

  // |x-a|
  FUNC add_abs(FUNC &f, T a) {
    f = add_a_minus_x(f, a);
    f = add_x_minus_a(f, a);
    return f;
  }

  // fx,x
  pair<T, T> get_min(FUNC &f) {
    if (f.x0 > f.x1) return {infty<T>, 0};
    if (f.a0 >= 0) {
      return {f.y0, f.x0};
    }
    auto [l, r] = ST.split_max_right_prod(
        f.root, [&](auto prod) -> bool { return f.a0 + prod.fi < 0; });
    auto [asum, xasum] = ST.prod(l);
    T x = (r ? ST.get(r, 0).fi : f.x1);
    f.root = ST.merge(l, r);
    T y = f.y0 + f.a0 * (x - f.x0) + x * asum - xasum;
    return {y, x};
  }

  FUNC clear_right(FUNC &f) {
    if (f.a0 >= 0) {
      ST.free_subtree(f.root), f.root = nullptr, f.a0 = 0;
      return f;
    }
    auto [l, r] = ST.split_max_right_prod(
        f.root, [&](auto prod) -> bool { return f.a0 + prod.fi < 0; });
    f.root = l;
    if (!r) {
      return f;
    }
    T x = ST.get(r, 0).fi;
    ST.free_subtree(r);
    f.root = ST.merge(f.root, ST.new_node({x, -(f.a0 + ST.prod(l).fi)}));
    return f;
  }
  FUNC clear_left(FUNC &f) {
    if (f.a0 >= 0) {
      return f;
    }
    auto [l, r] = ST.split_max_right_prod(
        f.root, [&](auto prod) -> bool { return f.a0 + prod.fi < 0; });
    auto [asum, xasum] = ST.prod(l);
    if (!r) {
      // 定数にする
      T x = f.x1;
      T y = f.y0 + f.a0 * (x - f.x0) + x * asum - xasum;
      ST.free_subtree(l);
      f.root = nullptr;
      f.y0 = y, f.a0 = 0;
      return f;
    }
    T x = ST.get(f.root, 0).fi;
    T y = f.y0 + f.a0 * (x - f.x0) + x * asum - xasum;
    T a = f.a0 + asum + ST.get(r, 0).se;
    ST.free_subtree(l);
    f.root = r;
    ST.set(r, 0, {x, a});
    f.y0 = y;
    f.a0 = 0;
    return f;
  }
#ifdef FASTIO
  void debug(FUNC &f) {
    auto dat = ST.get_all(f.root);
    SHOW(f.x0, f.x1, f.a0, f.y0);
    SHOW(dat);
  }
#endif
};
}  // namespace SLOPE_TRICK_SUPER
using SLOPE_TRICK_SUPER::Slope_Trick_Super;
//https://maspypy.github.io/library/convex/slope_trick/slope_super.hpp
void solve(){
  ll n,k;
  cin>>n>>k;
  vc<ll>a(n),b(n),c(n),d(n);
  for(int i=0;i<n;i++)cin>>a[i];
  for(int i=0;i<n;i++)cin>>b[i];
  for(int i=0;i<n;i++)cin>>c[i];
  for(int i=0;i<n;i++)cin>>d[i];

  Slope_Trick_Super<ll>sp;
  using F=Slope_Trick_Super<ll>::FUNC;
  F s=sp.segment_func(0,k,1e12,0);
  for(int i=0;i<n;i++){
    s=sp.convolve_segment(s,0,b[i],a[i],0);
    s=sp.convolve_segment(s,-d[i],0,c[i],0);
    s=sp.restrict_domain(s,0,k);
  }
  auto res=sp.get_min(s);
  cout<<-res.first<<"\n";
}
signed main(){
    cin.tie(0)->sync_with_stdio(0);
    cout<<fixed<<setprecision(20);
    int t=1;
  cin >> t;
    while(t--)solve();
}