#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

typedef int _loop_int;
#define REP(i,n) for(_loop_int i=0;i<(_loop_int)(n);++i)
#define FOR(i,a,b) for(_loop_int i=(_loop_int)(a);i<(_loop_int)(b);++i)
#define FORR(i,a,b) for(_loop_int i=(_loop_int)(b)-1;i>=(_loop_int)(a);--i)

#define DEBUG(x) cout<<#x<<": "<<x<<endl
#define DEBUG_VEC(v) cout<<#v<<":";REP(i,v.size())cout<<" "<<v[i];cout<<endl
#define ALL(a) (a).begin(),(a).end()

#define CHMIN(a,b) a=min((a),(b))
#define CHMAX(a,b) a=max((a),(b))

// mod
const ll MOD = 1000000007ll;
#define FIX(a) ((a)%MOD+MOD)%MOD

// floating
typedef double Real;
const Real EPS = 1e-11;
#define EQ0(x) (abs(x)<EPS)
#define EQ(a,b) (abs(a-b)<EPS)
typedef complex<Real> P;

int gx,gy;
int k;
int x[5],y[5],n[5];

ll ans;

ll fact[125];
ll ifact[25];

void dfs(vi V){
  if(V.size()==k){
    // calc
    int xx = 0, yy = 0;
    int sum = 0;
    REP(i,k)sum += V[i];
    ll yo = fact[sum];
    REP(i,k){
      xx += x[i]*V[i];
      yy += y[i]*V[i];
      yo *= ifact[V[i]];
    }
    if(xx==gx && yy==gy)ans = (ans+yo)%MOD;
  }else{
    int i = V.size();
    REP(j,n[i]+1){
      vi W = V;
      W.push_back(j);
      dfs(W);
    }
  }
}

int main(){
  scanf("%d%d%d",&gx,&gy,&k);
  REP(i,k)scanf("%d%d%d",x+i,y+i,n+i);
  fact[0] = 1;
  FOR(i,1,125)fact[i] = fact[i-1]*i%MOD;
  ifact[0] = 1;
  FOR(i,1,25){
    ll inv = 1;
    while(inv%i != 0){
      inv += MOD;
    }
    inv /= i;
    ifact[i] = ifact[i-1] * inv % MOD;
  }
  dfs(vi());
  printf("%lld\n",ans);
  return 0;
}