This documentation is automatically generated by online-judge-tools/verification-helper
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2397"
#include<bits/stdc++.h>
using namespace std;
#define call_from_test
#include "../../linearalgebra/squarematrix.cpp"
#include "../../mod/mint.cpp"
#undef call_from_test
#ifdef SANITIZE
#define IGNORE
#endif
signed main(){
cin.tie(0);
ios::sync_with_stdio(0);
const int MAX = 80;
const int MOD = 1e9+9;
using M = Mint<int, MOD>;
using SM = SquareMatrix<M, MAX>;
using ll = long long;
ll w,h,n;
ll cnt=0;
while(cin>>w>>h>>n,w){
vector<ll> x(n),y(n);
for(int i=0;i<n;i++) cin>>x[i]>>y[i];
{
using P = pair<ll, ll>;
vector<P> vp;
for(int i=0;i<n;i++) vp.emplace_back(y[i],x[i]);
sort(vp.begin(),vp.end());
for(int i=0;i<n;i++) tie(y[i],x[i])=vp[i];
}
SM b;
for(int i=0;i<w;i++){
b[i][i]=M(1);
if(i-1>=0) b[i][i-1]=M(1);
if(i+1<w) b[i][i+1]=M(1);
}
ll d=1;
SM res=SM::mul_identity();
for(int k=0;k<n;k++){
if(y[k]==d) continue;
res=b.pow(y[k]-d-1)*res;
int j=k;
SM c(b);
while(j<n&&y[k]==y[j]){
for(int i=0;i<w;i++) c[x[j]-1][i]=0;
j++;
}
res=c*res;
d=y[k];
}
res=b.pow(h-d)*res;
cout<<"Case "<<++cnt<<": "<<res[w-1][0].v<<endl;
}
return 0;
}
#line 1 "test/aoj/2397.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2397"
#include<bits/stdc++.h>
using namespace std;
#define call_from_test
#line 1 "linearalgebra/squarematrix.cpp"
#line 3 "linearalgebra/squarematrix.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
template<typename R, size_t N>
struct SquareMatrix{
typedef array<R, N> arr;
typedef array<arr, N> mat;
mat dat;
SquareMatrix(){
for(size_t i=0;i<N;i++)
for(size_t j=0;j<N;j++)
dat[i][j]=R::add_identity();
}
bool operator==(const SquareMatrix& a) const{
return dat==a.dat;
}
size_t size() const{return N;}
arr& operator[](size_t k){return dat[k];}
const arr& operator[](size_t k) const {return dat[k];}
static SquareMatrix add_identity(){return SquareMatrix();}
static SquareMatrix mul_identity(){
SquareMatrix res;
for(size_t i=0;i<N;i++) res[i][i]=R::mul_identity();
return res;
}
SquareMatrix operator*(const SquareMatrix &B) const{
SquareMatrix res;
for(size_t i=0;i<N;i++)
for(size_t j=0;j<N;j++)
for(size_t k=0;k<N;k++)
res[i][j]=res[i][j]+(dat[i][k]*B[k][j]);
return res;
}
SquareMatrix operator+(const SquareMatrix &B) const{
SquareMatrix res;
for(size_t i=0;i<N;i++)
for(size_t j=0;j<N;j++)
res[i][j]=dat[i][j]+B[i][j];
return res;
}
SquareMatrix pow(long long n) const{
SquareMatrix a=*this,res=mul_identity();
while(n){
if(n&1) res=res*a;
a=a*a;
n>>=1;
}
return res;
}
};
//END CUT HERE
#ifndef call_from_test
//INSERT ABOVE HERE
signed main(){
return 0;
}
#endif
#line 1 "mod/mint.cpp"
#line 3 "mod/mint.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
template<typename T, T MOD = 1000000007>
struct Mint{
inline static constexpr T mod = MOD;
T v;
Mint():v(0){}
Mint(signed v):v(v){}
Mint(long long t){v=t%MOD;if(v<0) v+=MOD;}
Mint pow(long long k){
Mint res(1),tmp(v);
while(k){
if(k&1) res*=tmp;
tmp*=tmp;
k>>=1;
}
return res;
}
static Mint add_identity(){return Mint(0);}
static Mint mul_identity(){return Mint(1);}
Mint inv(){return pow(MOD-2);}
Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;}
Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;}
Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;}
Mint& operator/=(Mint a){return (*this)*=a.inv();}
Mint operator+(Mint a) const{return Mint(v)+=a;}
Mint operator-(Mint a) const{return Mint(v)-=a;}
Mint operator*(Mint a) const{return Mint(v)*=a;}
Mint operator/(Mint a) const{return Mint(v)/=a;}
Mint operator+() const{return *this;}
Mint operator-() const{return v?Mint(MOD-v):Mint(v);}
bool operator==(const Mint a)const{return v==a.v;}
bool operator!=(const Mint a)const{return v!=a.v;}
static Mint comb(long long n,int k){
Mint num(1),dom(1);
for(int i=0;i<k;i++){
num*=Mint(n-i);
dom*=Mint(i+1);
}
return num/dom;
}
};
template<typename T, T MOD>
ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;}
//END CUT HERE
#ifndef call_from_test
signed main(){
return 0;
}
#endif
#line 9 "test/aoj/2397.test.cpp"
#undef call_from_test
#ifdef SANITIZE
#define IGNORE
#endif
signed main(){
cin.tie(0);
ios::sync_with_stdio(0);
const int MAX = 80;
const int MOD = 1e9+9;
using M = Mint<int, MOD>;
using SM = SquareMatrix<M, MAX>;
using ll = long long;
ll w,h,n;
ll cnt=0;
while(cin>>w>>h>>n,w){
vector<ll> x(n),y(n);
for(int i=0;i<n;i++) cin>>x[i]>>y[i];
{
using P = pair<ll, ll>;
vector<P> vp;
for(int i=0;i<n;i++) vp.emplace_back(y[i],x[i]);
sort(vp.begin(),vp.end());
for(int i=0;i<n;i++) tie(y[i],x[i])=vp[i];
}
SM b;
for(int i=0;i<w;i++){
b[i][i]=M(1);
if(i-1>=0) b[i][i-1]=M(1);
if(i+1<w) b[i][i+1]=M(1);
}
ll d=1;
SM res=SM::mul_identity();
for(int k=0;k<n;k++){
if(y[k]==d) continue;
res=b.pow(y[k]-d-1)*res;
int j=k;
SM c(b);
while(j<n&&y[k]==y[j]){
for(int i=0;i<w;i++) c[x[j]-1][i]=0;
j++;
}
res=c*res;
d=y[k];
}
res=b.pow(h-d)*res;
cout<<"Case "<<++cnt<<": "<<res[w-1][0].v<<endl;
}
return 0;
}