Language: C++

#include <bits/stdc++.h>

using namespace std;

#define DEBUG(x) cerr<<#x<<": "<<x<<endl;
#define DEBUG_VEC(v) cerr<<#v<<":";for(int i=0;i<v.size();i++) cerr<<" "<<v[i]; cerr<<endl

typedef long long ll;
#define vi vector<int>
#define vl vector<ll>
#define vii vector< vector<int> >
#define vll vector< vector<ll> >
#define vs vector<string>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define pll pair<ll,ll>
template<class S, class T> pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first + t.first, s.second + t.second); }
template<class S, class T> pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template<class S, class T> ostream& operator<<(ostream& os, pair<S, T> p) { os << "(" << p.first << ", " << p.second << ")"; return os; }
#define X first
#define Y second
#define rep(i,n) for(int i=0;i<(n);i++)
#define rep1(i,n) for(int i=1;i<=(n);i++)
#define rrep(i,n) for(int i=(n)-1;i>=0;i--)
#define rrep1(i,n) for(int i=(n);i>0;i--)
#define REP(i,a,b) for(int i=a;i<b;i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(),c.end()
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a = b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a = b; return 1; } return 0; }
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = 1e18;
const ll MOD = 1000000007;
//const ll MOD = 998244353;
const double pi = 3.14159265358979323846;
#define Sp(p) cout<<setprecision(15)<< fixed<<p<<endl;
int dx[4] = { 1,0, -1,0 }, dy[4] = { 0,1,0,-1 };
int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
#define fio() cin.tie(0); ios::sync_with_stdio(false);
//#define mp make_pair

const int MAXN = 200010;

vl fact(MAXN);
vl rfact(MAXN);

ll mod_pow(ll x, ll p, ll M = MOD) {
	ll a = 1;
	while (p) {
		if (p % 2)
			a = a*x%M;
		x = x*x%M;
		p /= 2;
	}
	return a;
}

ll mod_inverse(ll a, ll M = MOD) {
	return mod_pow(a, M - 2, M);
}

void set_fact(ll n, ll M = MOD) {
	fact[0] = fact[1] = rfact[0] = rfact[1] = 1;
	for (ll i = 2; i <= n; i++) {
		fact[i] = i * fact[i - 1] % M;
		rfact[i] = mod_inverse(fact[i], M);
	}
}

//http://drken1215.hatenablog.com/entry/2018/06/08/210000
//nが大きくfactが計算できないときのほかの計算方法について書いてある
ll nCr(ll n, ll r, ll M = MOD) {
  if (r > n) return 0;
  if (r < 0 || n < 0) return 0;
  ll ret = fact[n];
  ret = (ret*rfact[r]) % M;
  ret = (ret*rfact[n - r]) % M;
  return ret;
}



int main() {
  int h, w, n;
  cin >> h >> w >> n;
  set_fact(2*max(h, w));
  vector<pll> rc(n);
  rep (i, n) {
    cin >> rc[i].first >> rc[i].second;
    rc[i] = rc[i] - pii(1, 1);
  }
  sort(all(rc));
  vl dp(n + 1);
  dp[0] = 1;
  rep (i, n) {
    ll r = rc[i].first, c = rc[i].second;
    dp[i + 1] = nCr(r + c, r) % MOD;
    for (int j = 0; j < i; j++) {
      int r2 = rc[j].first, c2 = rc[j].second;
      if (r2 <= r && c2 <= c) {
        (dp[i + 1] -= dp[j] * nCr(r - r2 + c - c2, r - r2) % MOD) %= MOD;
      }
    }
  }
  ll ans = nCr(h + w - 2, h - 1) % MOD;
  rep (i, n) {
    ll r = rc[i].first, c = rc[i].second;
    (ans -= dp[i + 1] * nCr(h - 1 - r + w - 1 - c, h - 1 - r) % MOD) %= MOD;
  }
  ans = (ans + MOD) % MOD;
  cout << ans << endl;
}


Compiler output:
a.cc: In function 'int main()':
a.cc:92:19: error: no match for 'operator-' (operand types are '__gnu_cxx::__alloc_traits<std::allocator<std::pair<long long int, long long int> >, std::pair<long long int, long long int> >::value_type' {aka 'std::pair<long long int, long long int>'} and 'std::pair<int, int>')
   92 |     rc[i] = rc[i] - pii(1, 1);
a.cc:19:39: note: candidate: 'template<class S, class T> std::pair<_T1, _T2> operator-(const std::pair<_T1, _T2>&, const std::pair<_T1, _T2>&)'
   19 | template<class S, class T> pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
      |                                       ^~~~~~~~
a.cc:19:39: note:   template argument deduction/substitution failed:
a.cc:92:29: note:   deduced conflicting types for parameter '_T1' ('long long int' and 'int')
   92 |     rc[i] = rc[i] - pii(1, 1);
      |                             ^
In file included from /usr/include/c++/14/bits/stl_algobase.h:67,
                 from /usr/include/c++/14/algorithm:60,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:51,
                 from a.cc:1:
/usr/include/c++/14/bits/stl_iterator.h:618:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr decltype ((__y.base() - __x.base())) std::operator-(const reverse_iterator<_Iterator>&, const reverse_iterator<_IteratorR>&)'
  618 |     operator-(const reverse_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:618:5: note:   template argument deduction/substitution failed:
a.cc:92:29: note:   '__gnu_cxx::__alloc_traits<std::allocator<std::pair<long long int, long long int> >, std::pair<long long int, long long int> >::value_type' {aka 'std::pair<long long int, long long int>'} is not derived from 'const std::reverse_iterator<_Iterator>'
   92 |     rc[i] = rc[i] - pii(1, 1);
      |                             ^
/usr/include/c++/14/bits/stl_iterator.h:1790:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr decltype ((__x.base() - __y.base())) std::operator-(const move_iterator<_IteratorL>&, const move_iterator<_IteratorR>&)'
 1790 |     operator-(const move_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1790:5: note:   template argument deduction/substitution failed:
a.cc:92:29: note:   '__gnu_cxx::__alloc_traits<std::allocator<std::pair<long long int, long long int> >, std::pair<long long int, long long int> >::value_type' {aka 'std::pair<long long int, long long int>'} is not derived from 'const std::move_iterator<_IteratorL>'
   92 |     rc[i] = rc[i] - pii(1, 1);
      |                             ^
In file included from /usr/include/c++/14/ccomplex:39,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:127:
/usr/include/c++/14/complex:370:5: note: candidate: 'template<class _Tp> std::complex<_Tp> std::operator-(const complex<_Tp>&, const complex<_Tp>&)'
  370 |     operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
      |     ^~~~~~~~
/usr/include/c++/14/complex:370:5: note:   template argument deduction/substitution failed:
a.cc:92:29: note:   '__gnu_cxx::__alloc_traits<std::allocator<std::pair<long long int, long long int> >, std::pair<long long int, long long int> >::value_type' {aka 'std::pair<long long int, long long int>'} is not derived from 'const std::complex<_Tp>'
   92 |     rc[i] = rc[i] - pii(1, 1);
      |                             ^
/usr/include/c++/14/complex:379:5: note: candidate: 'template<class _Tp> std::complex<_Tp> std::operator-(const complex<_Tp>&, const _Tp&)'
  379 |     operator-(const complex<_Tp>& __x, const _Tp& __y)
      |     ^~~~~~~~
/usr/include/c++/14/complex:379:5: note:   template argument deduction/substitution failed:
a.cc:92:29: note:   '__gnu_cxx::__alloc_traits<std::allocator<std::pair<long long int, long long int> >, std::pair<long long int, long long int> >::value_type' {aka 'std::pair<long long int, long long int>'} is not derived from 'const std::complex<_Tp>'
   92 |     rc[i] = rc[i] - pii(1, 1);
      |                             ^
/usr/include/c++/14/complex:388:5: note: candidate: 'template<class _Tp> std::complex<_Tp> std::operator-(const _Tp&, const complex<_Tp>&)'
  388 |     operator-(const _Tp& __x, const complex<_Tp>& __y)
      |     ^~~~~~~~
/usr/include/c++/14/complex:388:5: note:   template argument deduction/substitution failed:
a.cc:92:29: note:   'std::pair<int, int>' is not derived from 'const std::complex<_Tp>'
   92 |     rc[i] = rc[i] - pii(1, 1);
      |                             ^
/usr/include/c++/14/complex:465:5: note: candidate: 'template<class _Tp> std::complex<_Tp> std::operator-(const complex<_Tp>&)'
  465 |     operator-(const complex<_Tp>& __x)
      |     ^~~~~~~~
/usr/include/c++/14/complex:465:5: note:   candidate expects 1 argument, 2 provided
In file included from /usr/include/c++/14/valarray:605,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:166:
/usr/include/c++/14/bits/valarray_after.h:406:5: note: candidate: 'template<class _Dom1, class _Dom2> std::_Expr<std::__detail::_BinClos<std::__minus, std::_Expr, std::_Expr, _Dom1, _Dom2>, typename std::__fun<std::__minus, typename _Dom1::value_type>::result_type> std::operator-(const _Expr<_Dom1, typename _Dom1::value_type>&, const _Expr<_Dom2, typename _Dom2::value_type>&)'
  406 |     _DEFINE_EXPR_BINARY_OPERATOR(-, struct std::__minus)
      |     ^~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/valarray_after.h:406:5: note:   template argument deduction/substitution failed:
a.cc:92:29: note:   '__gnu_cxx::__alloc_traits<std::allocator<std::pair<long long int, long long int> >, std::pair<long long int, long long int> >::value_type' {aka 'std::pair<long long int, long long int>'} is not derived from 'const std::_Expr<_Dom1, typename _Dom1::value_type>'
   92 |     rc[i] = rc[i] - pii(1, 1);
      |                             ^
/usr/include/c++/14/bits/valarray_after.h:406:5: note: candidate: 'template<class _Dom> std::_Expr<std::__detail::_BinClos<std::__minus, std::_Expr, std::_Constant, _Dom, typename _Dom::value_type>, typename std::__fun<std::__minus, typename _Dom1::value_type>::result_type> std::operator-(const _Expr<_Dom1, typename _Dom1::value_type>&, const typename _Dom::value_type&)'
  406 |     _DEFINE_EXPR_BINARY_OPERATOR(-, struct std::__minus)
      |     ^~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/valarray_after.h:406:5: note:   template argument deduction/substitution failed:
a.cc:92:29: note:   '__gnu_cxx::__alloc_traits<std::allocator<std::pair<long long int, long long int> >, std::pair<long long int, long long int> >::value_type' {aka 'std::pair<long long int, long long int>'} is not derived from 'const std::_Expr<_Dom1, typename _Dom1::value_type>'
   92 |     rc[i] = rc[i] - pii(1, 1);
      |                             ^
/usr/include/c++/14/bits/valarray_after.h:406:5: note: candidate: 'template<class _Dom> std::_Expr<std::__detail::_BinClos<std::__minus, std::_Constant, std::_Expr, typename _Dom::value_type, _Dom>, typename std::__fun<std::__minus, typename _Dom1::value_type>::result_type> std::operator-(const typename _Dom::value_type&, const _Expr<_Dom1, typename _Dom1::value_type>&)'
  406 |     _DEFINE_EXPR_BINARY_OPERATOR(-, struct std::__minus)
      |     ^~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/valarray_after.h:406:5: note:   template argument deduction/substitution failed:
a.cc:92:29: note:   'std::pair<int, int>' is not derived from 'const std::_Expr<_Dom1, typename _Dom1::value_type>'
   92 |     rc[i] = rc[i] - pii(1, 1);
      |                             ^
/usr/include/c++/14/bits/valarray_after.h:406:5: note: candidate: 'template<class _Dom> std::_Expr<std::__detail::_BinClos<std::__minus, std::_Expr, std::_ValArray, _Dom, typename _Dom::value_type>, typename std::__fun<std::__minus, typename _Dom1::value_type>::result_type> std::operator-(const _Expr<_Dom1, typename _Dom1::value_type>&, const valarray<typename _Dom::value_type>&)'
  406 |     _DEFINE_EXPR_BINARY_OPERATOR(-, struct std::__minus)
      |     ^~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/valarray_after.h:406:5: note:   template argument deduction/substitution failed:
a.cc:92:29: note:   '__gnu_cxx::__alloc_traits<std::allocator<std::pair<long long int, long long int> >, std::pair<long long int, long long int> >::value_type' {aka 'std::pair<long long int, long long int>'} is not derived from 'const std::_Expr<_Dom1, typename _Dom1::value_type>'
   92 |     rc[i] = rc[i] - pii(1, 1);
      |                             ^
/usr/include/c++/14/bits/valarray_after.h:406:5: note: candidate: 'template<class _Dom> std::_Expr<std::__detail::_BinClos<std::__minus, std::_ValArray, std::_Expr, typename _Dom::value_type, _Dom>, typename std::__fun<std::__minus, typename _Dom1::value_type>::result_type> std::operator-(const valarray<typename _Dom::value_type>&, const _Expr<_Dom1, typename _Dom1::value_type>&)'
  406 |     _DEFINE_EXPR_BINARY_OPERATOR(-, struct std::__minus)
      |     ^~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/valarray_after.h:406:5: note:   template argument deduction/substitution failed:
a.cc:92:29: note:   'std::pair<int, int>' is not derived from 'const std::_Expr<_Dom1, typename _Dom1::value_type>'
   92 |     rc[i] = rc[i] - pii(1, 1);
      |                             ^
/usr/include/c++/14/valarray:1197:1: note: candidate: 'template<class _Tp> std::_Expr<std::__detail::_BinClos<std::__minus, std::_ValArray, std::_ValArray, _Tp, _Tp>, typename std::__fun<std::__minus, _Tp>::result_type> std::operator-(const valarray<_Tp>&, const valarray<_Tp>&)'
 1197 | _DEFINE_BINARY_OPERATOR(-, __minus)
      | ^~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/valarray:1197:1: note:   template argument deduction/substitution failed:
a.cc:92:29: note:   '__gnu_cxx::__alloc_traits<std::allocator<std::pair<long long int, long long int> >, std::pair<long long int, long long int> >::value_type' {aka 'std::pair<long long int, long long int>'} is not derived from 'const std::valarray<_Tp>'
   92 |     rc[i] = rc[i] - pii(1, 1);
      |