// GRUNDY GRAPH // Official 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-9; 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 2000002 struct edge{int e, nxt;}; int V, E; edge e[LIM], er[LIM]; int sp[LIM], spr[LIM]; int group_cnt, comp[LIM]; bool v[LIM]; int stk[LIM]; void fill_forward(int x) { int i; v[x]=true; for(i=sp[x];i;i=e[i].nxt) if(!v[e[i].e]) fill_forward(e[i].e); stk[++stk[0]]=x; } void fill_backward(int x) { int i; v[x]=false; comp[x]=group_cnt; for(i=spr[x];i;i=er[i].nxt) if(v[er[i].e]) fill_backward(er[i].e); } void add_edge(int v1, int v2) //add edge v1->v2 { e [++E].e=v2; e [E].nxt=sp [v1]; sp [v1]=E; er[ E].e=v1; er[E].nxt=spr[v2]; spr[v2]=E; } void SCC() { int i; stk[0]=0; memset(v, false, sizeof(v)); for(i=1;i<=V;i++) if(!v[i]) fill_forward(i); group_cnt=0; for(i=stk[0];i>=1;i--) if(v[stk[i]]){group_cnt++; fill_backward(stk[i]);} } int val[LIM]; bool visA[LIM],visB[LIM]; vector con[LIM]; bool rec(int s,int i) { if ((i!=s) && ((i-1)/2%2)) return(1); if (visB[i]) return(0); visB[i]=1; int j; Fox(j,Sz(con[i])) if (rec(s,con[i][j])) return(1); return(0); } int main() { if (DEBUG) freopen("in.txt","r",stdin); int T,t; int N,M; int i,j,a,b; Read(T); Fox1(t,T) { printf("Case #%d: ",t); Read(N),Read(M); N<<=1; Fox1(i,N) con[i].clear(); V=N; E=0; Fill(sp,0); Fill(spr,0); while (M--) { Read(i),Read(j); con[i].pb(j); add_edge(i,j); if (j%2) j++; else j--; if (i%2) i++; else i--; con[j].pb(i); add_edge(j,i); } SCC(); Fill(visA,0); Fill(visB,0); Fox1(i,N) { //Alice a=comp[i],b=comp[i+1]; if (a==b) goto Bad; visA[a]=visA[b]=1; i+=2; //Bob a=comp[i],b=comp[i+1]; if ((visA[a]) || (visA[b]) || (rec(i,i)) || (rec(i+1,i+1))) goto Bad; i++; } printf("Alice\n"); continue; Bad:; printf("Bob\n"); } return(0); }