2020/round2/log_drivin_hirin.cpp

// Log Drivin' Hirin'
// Solution by Jacob Plachta

#include <algorithm>
#include <functional>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <complex>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <cassert>
#include <string>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <sstream>
using namespace std;

#define LL long long
#define LD long double
#define PR pair<int,int>

#define Fox(i,n) for (i=0; i<n; i++)
#define Fox1(i,n) for (i=1; i<=n; i++)
#define FoxI(i,a,b) for (i=a; i<=b; i++)
#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
#define FoxR1(i,n) for (i=n; i>0; i--)
#define FoxRI(i,a,b) for (i=b; i>=a; i--)
#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
#define Min(a,b) a=min(a,b)
#define Max(a,b) a=max(a,b)
#define Sz(s) int((s).size())
#define All(s) (s).begin(),(s).end()
#define Fill(s,v) memset(s,v,sizeof(s))
#define pb push_back
#define mp make_pair
#define x first
#define y second

template<typename T> T Abs(T x) { return(x < 0 ? -x : x); }
template<typename T> T Sqr(T x) { return(x * x); }
string plural(string s) { return(Sz(s) && s[Sz(s) - 1] == 'x' ? s + "en" : s + "s"); }

const int INF = (int)1e9;
const LD EPS = 1e-12;
const LD PI = acos(-1.0);

#define GETCHAR getchar_unlocked

bool Read(int& x) {
  char c, r = 0, n = 0;
  x = 0;
  for (;;) {
    c = GETCHAR();
    if ((c < 0) && (!r))
      return(0);
    if ((c == '-') && (!r))
      n = 1;
    else if ((c >= '0') && (c <= '9'))
      x = x * 10 + c - '0', r = 1;
    else if (r)
      break;
  }
  if (n)
    x = -x;
  return(1);
}

struct Line {
  mutable LL k, m, p;
  bool operator<(const Line& o) const { return k < o.k; }
  bool operator<(LL x) const { return p < x; }
};

struct LineContainer : multiset<Line, less<>> {
  const LL inf = LLONG_MAX;
  LL div(LL a, LL b) { // floored division
    return a / b - ((a ^ b) < 0 && a % b);
  }
  bool isect(iterator x, iterator y) {
    if (y == end()) { x->p = inf; return false; }
    if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
    else x->p = div(y->m - x->m, x->k - y->k);
    return x->p >= y->p;
  }
  void add(LL k, LL m) {
    auto z = insert({ k, m, 0 }), y = z++, x = y;
    while (isect(y, z)) z = erase(z);
    if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
    while ((y = x) != begin() && (--x)->p >= y->p)
      isect(x, erase(y));
  }
  LL query(LL x) {
    assert(!empty());
    auto l = *lower_bound(x);
    return l.k * x + l.m;
  }
};

#define LIM 1000001
#define MOD 1000000007

int N, M, K, ans;
int P[LIM], L[LIM], H[LIM], X[LIM], Y[LIM];
vector<int> ch[LIM], Q[LIM];
int nid, id[LIM];
LineContainer LC[LIM];

void ReadSeq(int* V, int N, int K, int mod)
{
  int i, A, B, C;
  Fox(i, K)
    Read(V[i]);
  Read(A), Read(B), Read(C);
  if (!mod)
    Read(mod);
  FoxI(i, K, N - 1)
    V[i] = ((LL)A * V[i - 2] + (LL)B * V[i - 1] + C) % (mod < 0 ? i : mod) + 1;
}

LL GetQueryAns(int i, LL d, int c)
{
  return(c * d + LC[id[i]].query(c));
}

void rec(int i, LL d)
{
  // init new line container
  id[i] = nid++;
  // recurse to children
  for (auto c : ch[i])
  {
    rec(c, d + L[c]);
    // merge smaller line container into larger one
    int& a = id[i], & b = id[c];
    if (Sz(LC[a]) < Sz(LC[b]))
      swap(a, b);
    for (auto ln : LC[b])
      LC[a].add(ln.k, ln.m);
    LC[b].clear();
  }
  // add line for hireable log driver or leaf node
  LC[id[i]].add(-d, Sz(ch[i]) ? GetQueryAns(i, d, H[i]) : 0);
  // answer queries at this node
  for (auto c : Q[i])
    ans = ans * ((-GetQueryAns(i, d, c) + 1) % MOD) % MOD;
  ch[i].clear(), Q[i].clear();
}

int ProcessCase()
{
  int i;
  // input
  Read(N), Read(M), Read(K);
  ReadSeq(P, N, K, -1);
  ReadSeq(L, N, K, 0);
  ReadSeq(H, N, K, 0);
  ReadSeq(X, M, K, N);
  ReadSeq(Y, M, K, 0);
  // init tree/queries
  Fox1(i, N - 1)
    ch[P[i] - 1].pb(i);
  Fox(i, M)
    Q[X[i] - 1].pb(Y[i]);
  // compute answers
  ans = 1;
  nid = 0;
  rec(0, 0);
  LC[id[0]].clear();
  return(ans);
}

int main() {
  int T, t;
  Read(T);
  Fox1(t, T)
    printf("Case #%d: %d\n", t, ProcessCase());
  return(0);
}