Problem:
Score : 100 points

Problem Statement

There is a grid with H horizontal rows and W vertical columns.
Let (i, j) denote the square at the i-th row from the top and the j-th column from the left.

In the grid, N Squares (r_1, c_1), (r_2, c_2), \ldots, (r_N, c_N) are wall squares, and the others are all empty squares.
It is guaranteed that Squares (1, 1) and (H, W) are empty squares.

Taro will start from Square (1, 1) and reach (H, W) by repeatedly moving right or down to an adjacent empty square.

Find the number of Taro's paths from Square (1, 1) to (H, W), modulo 10^9 + 7.

Constraints

All values in input are integers.

2 \leq H, W \leq 10^5

1 \leq N \leq 3000

1 \leq r_i \leq H

1 \leq c_i \leq W

Squares (r_i, c_i) are all distinct.

Squares (1, 1) and (H, W) are empty squares.

Input

Input is given from Standard Input in the following format:

H W N
r_1 c_1
r_2 c_2
:
r_N c_N

Output

Print the number of Taro's paths from Square (1, 1) to (H, W), modulo 10^9 + 7.

Sample Input 1

3 4 2
2 2
1 4

Sample Output 1

3

There are three paths as follows:

Sample Input 2

5 2 2
2 1
4 2

Sample Output 2

0

There may be no paths.

Sample Input 3

5 5 4
3 1
3 5
1 3
5 3

Sample Output 3

24

Sample Input 4

100000 100000 1
50000 50000

Sample Output 4

123445622

Be sure to print the count modulo 10^9 + 7.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("unroll-loops")

#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;

#define ll long long
#define ull unsigned long long
#define ld long double
#define pii pair<int,int>
#define pll pair<ll,ll>
#define vi vector<int>
#define vll vector<ll>
#define vc vector<char>
#define vs vector<string>
#define vpll vector<pll>
#define vpii vector<pii>
#define umap unordered_map
#define uset unordered_set
#define PQ priority_queue

#define printa(a,L,R) for(int i=L;i<R;i++) cout<<a[i]<<(i==R-1?'\n':' ')
#define printv(a) printa(a,0,a.size())
#define print2d(a,r,c) for(int i=0;i<r;i++) for(int j=0;j<c;j++) cout<<a[i][j]<<(j==c-1?'\n':' ')
#define pb push_back
#define eb emplace_back
#define mt make_tuple
#define fbo find_by_order
#define ook order_of_key
#define MP make_pair
#define UB upper_bound
#define LB lower_bound
#define SQ(x) ((x)*(x))
#define issq(x) (((ll)(sqrt((x))))*((ll)(sqrt((x))))==(x))
#define F first
#define S second
#define mem(a,x) memset(a,x,sizeof(a))
#define inf 1e18
#define E 2.71828182845904523536
#define gamma 0.5772156649
#define nl "\n"
#define lg(r,n) (int)(log2(n)/log2(r))
#define pf printf
#define sf scanf
#define sf1(a)                scanf("%d",&a)
#define sf2(a,b)              scanf("%d %d",&a,&b)
#define sf3(a,b,c)            scanf("%d %d %d",&a,&b,&c)
#define pf1(a)                printf("%d\n",a);
#define pf2(a,b)              printf("%d %d\n",a,b)
#define pf3(a,b,c)            printf("%d %d %d\n",a,b,c)
#define sf1ll(a)              scanf("%lld",&a)
#define sf2ll(a,b)            scanf("%I64d %I64d",&a,&b)
#define sf3ll(a,b,c)          scanf("%I64d %I64d %I64d",&a,&b,&c)
#define pf1ll(a)              printf("%lld\n",a);
#define pf2ll(a,b)            printf("%I64d %I64d\n",a,b)
#define pf3ll(a,b,c)          printf("%I64d %I64d %I64d\n",a,b,c)
#define _ccase printf("Case %lld: ",++cs)
#define _case cout<<"Case "<<++cs<<": "
#define by(x) [](const auto& a, const auto& b) { return a.x < b.x; }

#define asche cerr<<"Ekhane asche\n";
#define rev(v) reverse(v.begin(),v.end())
#define srt(v) sort(v.begin(),v.end())
#define grtsrt(v) sort(v.begin(),v.end(),greater<ll>())
#define all(v) v.begin(),v.end()
#define mnv(v) *min_element(v.begin(),v.end())
#define mxv(v) *max_element(v.begin(),v.end())
#define toint(a) atoi(a.c_str())
#define BeatMeScanf ios_base::sync_with_stdio(false)
#define valid(tx,ty) (tx>=0&&tx<n&&ty>=0&&ty<m)
#define one(x) __builtin_popcount(x)
#define Unique(v) v.erase(unique(all(v)),v.end())
#define stree l=(n<<1),r=l+1,mid=b+(e-b)/2
#define fout(x) fixed<<setprecision(x)
string tostr(int n) {stringstream rr;rr<<n;return rr.str();}
inline void yes(){cout<<"YES\n";exit(0);}
inline void no(){cout<<"NO\n";exit(0);}
template <typename T> using o_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
//ll dx[]={1,0,-1,0,1,-1,-1,1};
//ll dy[]={0,1,0,-1,1,1,-1,-1};
//random_device rd;
//mt19937 rnd(rd());
#define debug(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator<string> _it(_ss); deb(_it, args); }
void deb(istream_iterator<string> it) {}
template<typename T, typename... Args>
void deb(istream_iterator<string> it, T a, Args... args) {
    cerr << *it << " = " << a << endl;
    deb(++it, args...);
}

const int mod=1e9+7;
const int N=3e5+9;
const ld eps=1e-9;
const ld PI=acos(-1.0);
//ll gcd(ll a,ll b){while(b){ll x=a%b;a=b;b=x;}return a;}
//ll lcm(ll a,ll b){return a/gcd(a,b)*b;}
ll qpow(ll n,ll k) {ll ans=1;assert(k>=0);n%=mod;while(k>0){if(k&1) ans=(ans*n)%mod;n=(n*n)%mod;k>>=1;}return ans%mod;}

int dp[N],f[N];
int ncr(int n,int r)
{
    int p=qpow(1LL*f[r]*f[n-r]%mod,mod-2);
    return 1LL*f[n]*p%mod;
}
pii a[N];
int main()
{
    BeatMeScanf;
    int i,j,k,n,m;
    f[0]=1;
    for(i=1;i<N;i++) f[i]=1LL*i*f[i-1]%mod;
    cin>>n>>m>>k;
    for(i=0;i<k;i++) cin>>a[i].F>>a[i].S;
    a[k].F=n;
    a[k].S=m;
    sort(a,a+k+1);
    for(i=0;i<=k;i++){
        dp[i]=ncr(a[i].F-1+a[i].S-1,a[i].F-1);
        for(j=0;j<i;j++){
            if(a[j].F<=a[i].F&&a[j].S<=a[i].S){
                dp[i]-=1LL*dp[j]*ncr(a[i].F-a[j].F+a[i].S-a[j].S,a[i].F-a[j].F)%mod;
                dp[i]=(dp[i]+mod)%mod;
            }
        }
    }
    cout<<dp[k]<<nl;
    return 0;
}
///Before submit=>
///    *check for integer overflow,array bounds
///    *check for n=1