// City Lights // Solution by Jacob Plachta #define DEBUG 0 #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); #if DEBUG #define GETCHAR getchar #else #define GETCHAR getchar_unlocked #endif 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 135 #define MOD 1000000007 int W,S,K,NH; PR PW[LIM],PS[LIM]; int H[LIM]; vector ch[LIM],wh[LIM]; LL dyn[LIM][LIM][LIM]; // dyn[i][h][b] = # of combinations in i's subtree requiring b buildings, with height h still required LL dynS[LIM][LIM][LIM]; // dynS[i][h][b] = sum of dyn[i][0..(h-1)][b] LL tmp[LIM][LIM]; void CompSums(int i) { int h,b; Fox(h,NH) Fox(b,W+1) dynS[i][h+1][b]=(dynS[i][h][b]+dyn[i][h][b])%MOD; } void Add(LL &a,LL b) { a=(a+b)%MOD; } void rec(int i) { int j,c,h,b,h2,b2,nw; LL pw; // iterate over children dyn[i][0][0]=1; Fox(j,Sz(ch[i])) { rec(c=ch[i][j]); // combine DP values CompSums(i),CompSums(c); Fill(tmp,0); Fox(h,NH) Fox(b,W+1) Fox(b2,W-b+1) Add(tmp[h][b+b2],dyn[i][h][b]*dynS[c][h+1][b2] + dynS[i][h][b]*dyn[c][h][b2]); memcpy(dyn[i],tmp,sizeof(tmp)); } // consider all possible subsets of windows coming into play here nw=Sz(wh[i]); sort(All(wh[i])); reverse(All(wh[i])); Fill(tmp,0); Fox(j,nw+1) { h2=(j==nw ? 0 : wh[i][j]); pw=(1LL<<(nw-min(nw,j+1)))%MOD; Fox(h,NH) Fox(b,W+1) Add(tmp[max(h,h2)][b],pw*dyn[i][h][b]); } memcpy(dyn[i],tmp,sizeof(tmp)); // place a building here when necessary FoxI(h,H[i],NH-1) Fox(b,W+1) { Add(dyn[i][0][b+1],dyn[i][h][b]); dyn[i][h][b]=0; } CompSums(i); } int main() { if (DEBUG) freopen("in.txt","r",stdin); // vars int T,t; int i,x,y,z,a,b,c; LL ans; vector cy; set > SI; set >::iterator I; map MS; // testcase loop Read(T); Fox1(t,T) { // input, and compress y-coordinates Read(W),Read(S); cy.clear(),cy.pb(0); Fox(i,W) Read(PW[i].y),Read(PW[i].x),cy.pb(PW[i].x); Fox(i,S) Read(PS[i].y),Read(PS[i].x),cy.pb(PS[i].x); sort(All(cy)); cy.resize(unique(All(cy))-cy.begin()); NH=Sz(cy); Fox(i,W) PW[i].x=lower_bound(All(cy),PW[i].x)-cy.begin(); Fox(i,S) PS[i].x=lower_bound(All(cy),PS[i].x)-cy.begin(); // init tree Fill(H,60); Fox(i,K) ch[i].clear(),wh[i].clear(); K=0; // iterate over stars in non-decreasing order of Y sort(PS,PS+S); SI.clear(); H[0]=1,SI.insert(mp(mp(0,INF+1),K++)); MS.clear(); Fox(i,S) { x=PS[i].y; y=PS[i].x; // find containing interval (if any) I=SI.lower_bound(mp(mp(x,INF+2),0)),I--; a=I->x.x; b=I->x.y; c=I->y; if ((a<=x) && (b>=x)) { // split interval at this X-coordinate if (ax) { ch[c].pb(K); H[K]=y,SI.insert(mp(mp(x+1,b),K++)); } SI.erase(I); MS[x]=c; } } // associate windows with nodes Fox(i,W) { x=PW[i].y; if (MS.count(x)) c=MS[x]; else { I=SI.lower_bound(mp(mp(x,INF+2),0)),I--; c=I->y; } wh[c].pb(PW[i].x); } // DP Fill(dyn,0); rec(0); ans=0; Fox1(i,W) Add(ans,i*dyn[0][0][i]); // output printf("Case #%d: %lld\n",t,ans); } return(0); }