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// SNAKE AND LADDER
// Official Solution by Jacob Plachta
#define DEBUG 0
#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 <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-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);
}
bool ReadLL(LL &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 MOD 1000000007
int main()
{
if (DEBUG)
freopen("in.txt","r",stdin);
int T,t;
LL N;
int K;
int i,ans;
LL a,b,x,y;
static pair<LL,int> P[1000];
Read(T);
Fox1(t,T)
{
ReadLL(N),Read(K);
Fox(i,K)
ReadLL(P[i].x),Read(P[i].y);
if (K==2*N-1)
{
ans=1;
goto Done;
}
sort(P,P+K);
a=1,b=N;
Fox(i,K-1)
if ((P[i].x==P[i+1].x) && (P[i].x==a))
a++;
FoxR(i,K-1)
if ((P[i].x==P[i+1].x) && (P[i].x==b))
b--;
ans=0;
Fox(i,K-1)
if ((P[i].x==P[i+1].x) && (P[i].x>=a) && (P[i].x<=b))
goto Done;
x=-1;
Fox(i,K)
if ((P[i].x>=a) && (P[i].x<=b))
if (x<0)
x=y=P[i].x;
else
{
if ((P[i].x-y)%2==(P[i].y+P[i-1].y)%2)
goto Done;
y=P[i].x;
}
if (x<0)
{
N=b-a+1;
if (N==1)
ans=2;
else
{
N=(N-1)%MOD;
ans=(4+2*N*(N+1))%MOD;
}
}
else
{
a=max(1LL,x-a);
b=max(1LL,b-y);
ans=2*(a%MOD)*(b%MOD)%MOD;
}
Done:;
printf("Case #%d: %d\n",t,ans);
}
return(0);
} |