// Circular Circles // Solution by Jacob Plachta #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define LL long long #define LD long double #define PR pair #define Fox(i,n) for (i=0; 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 T Abs(T x) { return(x < 0 ? -x : x); } template 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); } #define LIM 1000001 #define MOD 1000000007 int N, M, E, K; int X[LIM], Y[LIM], I[LIM], W[LIM], EW[LIM]; LL sumR; multiset CS[LIM]; // CS[i] = edge weights in circle i multiset HS[LIM][2]; // HS[i][j] = edge weights in half j of circle i multiset DS; // DS = circles' D values multiset IS; // IS = inter-circle edge weights 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); FoxI(i, K, N - 1) V[i] = ((LL)A * V[i - 2] + (LL)B * V[i - 1] + C) % mod; } void UpdateSet(multiset& S, int v1, int v2) { assert(*S.find(v1) == v1); S.erase(S.find(v1)); S.insert(v2); } int GetCircleR(int i) { return(*CS[i].rbegin()); } int GetCircleD(int i) { return(*HS[i][0].rbegin() + *HS[i][1].rbegin() - *CS[i].rbegin()); } int GetHalf(int i, int j) { return(X[i] <= j && j < Y[i] ? 0 : 1); } void UpdateCircleEdge(int i, int j, int w1, int w2) { int r1 = GetCircleR(i), d1 = GetCircleD(i); UpdateSet(CS[i], w1, w2); UpdateSet(HS[i][GetHalf(i, j)], w1, w2); int r2 = GetCircleR(i), d2 = GetCircleD(i); sumR += r2 - r1; UpdateSet(DS, d1, d2); } int ProcessCase() { int i, j; LL sumW; // init DS.clear(), IS.clear(); Fox(i, N) CS[i].clear(), HS[i][0].clear(), HS[i][1].clear(); // input Read(N), Read(M), Read(E), Read(K); ReadSeq(X, N, K, M); ReadSeq(Y, N, K, M); ReadSeq(I, E, K, N * M + N); ReadSeq(W, E, K, INF); // initialize edge info sumW = N * M + N; sumR = N; Fox(i, N * M + N) EW[i] = 1; Fox(i, N) { if (X[i] > Y[i]) swap(X[i], Y[i]); Fox(j, 2) HS[i][j].insert(0); Fox(j, M) { CS[i].insert(1); HS[i][GetHalf(i, j)].insert(1); } DS.insert(GetCircleD(i)); IS.insert(1); } // process events int ans = 1; Fox(i, E) { j = I[i]; int w1 = EW[j], w2 = W[i]; EW[j] = w2; sumW += w2 - w1; if (j < N * M) UpdateCircleEdge(j / M, j % M, w1, w2); else UpdateSet(IS, w1, w2); LL cur = sumW - sumR - max(*DS.rbegin(), *IS.rbegin()); ans = ans * (cur % MOD) % MOD; } return(ans); } int main() { int T, t; Read(T); Fox1(t, T) printf("Case #%d: %d\n", t, ProcessCase()); return(0); }