// Evening of the Living Dead // 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 3003 #define MOD 1000000007 int A[LIM],B[LIM]; PR GCD(int a,int b) { if (!b) return(mp(1,0)); PR p=GCD(b,a%b); return(mp(p.y,p.x-p.y*(a/b))); } int Add(int a,int b) { return((a+b)%MOD); } int Sub(int a,int b) { return((a-b+MOD)%MOD); } int Mult(int a,int b) { return((LL)a*b%MOD); } int Div(int a,int b) { int inv=GCD(b,MOD).x; if (inv<0) inv+=MOD; return(Mult(a,inv)); } int Prob(int i,int a,int b) { Max(a,A[i]); Min(b,B[i]); if (a>b) return(0); return(Div(b-a+1,B[i]-A[i]+1)); } int main() { if (DEBUG) freopen("in.txt","r",stdin); // vars int T,t; int N,M; int i,j,h,z,d,p,ans; int mH[LIM]; int nh,H[LIM]; static int dynSafe[LIM][LIM]; // [yard][max fence height protecting safe yard] static int dynZomb[LIM][LIM]; // [yard][max active zombie height] int aggr[LIM]; // testcase loop Read(T); Fox1(t,T) { // input Read(N),Read(M); Fox(i,N-1) Read(A[i]),Read(B[i]); Fill(mH,0); Fox(i,M) { Read(j),Read(h); Max(mH[j-1],h); } // coordinate compress zombie heights nh=0; H[nh++]=0; H[nh++]=INF; Fox(i,N) if (mH[i]) H[nh++]=mH[i]; sort(H,H+nh); nh=unique(H,H+nh)-H; Fox(i,N) mH[i]=lower_bound(H,H+nh,mH[i])-H; // DP Fill(dynSafe,0); Fill(dynZomb,0); if (mH[0]) dynZomb[1][mH[0]]=1; else dynSafe[1][0]=1; Fox1(i,N-1) { Fill(aggr,0); Fox(h,nh) { z=mH[i]; if (d=dynSafe[i][h]) { // new zombie's lower anyway? if ((!z) || (z=h) dynZomb[i+1][z]=Add(dynZomb[i+1][z],d); else { // prev zombie carrying over? p=Prob(i-1,0,H[h]); dynZomb[i+1][h]=Add(dynZomb[i+1][h],Mult(d,p)); // not carrying over? p=Sub(1,p); if (z) // new zombie dynZomb[i+1][z]=Add(dynZomb[i+1][z],Mult(d,p)); else // now safe dynSafe[i+1][0]=Add(dynSafe[i+1][0],Mult(d,p)); } } } // handle aggregated transitions d=0; Fox1(j,nh-1) { d=Add(d,aggr[j]); if (d) { p=Prob(i-1,H[j-1]+1,H[j]); dynSafe[i+1][j]=Add(dynSafe[i+1][j],Mult(d,p)); } } } // compute answer ans=0; Fox(h,nh) ans=Add(ans,dynSafe[N][h]); // output printf("Case #%d: %d\n",t,ans); } return(0); }