#include <iostream>
#include <algorithm>
#include <cstring>
#include <sstream>
#include <map>
#include <queue>
#include <set>
#include <vector>
#include <stack>
#include <cstdio>
#include <cmath>
#define mk make_pair
#define pb push_back
#define printf printf_s
#define scanf scanf_s
using namespace std;
typedef long long int ll;
typedef pair<ll, ll> pos;
const ll MOD = 1000000007, N = 200010, dx[4] = { -1,1,0,0 }, dy[4] = { 0,0,-1,1 }, MIN = -72340172838, MAX = 72340172838;

ll mn(ll a, ll b) {
	if (a == -1)return b;
	if (b == -1)return a;
	return min(a, b);
}
ll gcd(ll v1, ll v2) {
	if (v1 == 0)return v2; if (v2 == 0)return v1; if (v2 > v1)return gcd(v2%v1, v1); return gcd(v1%v2, v2);
}

ll pw(ll v1, ll v2) {
	ll v3 = 1;
	while (v2 > 0) {
		if (v2 % 2)v3 = (v3*v1) % MOD;
		v1 = (v1*v1) % MOD;
		v2 /= 2;
	}
	return v3;
}

struct ab {
	ll a, b;
	bool operator<(const ab& right) const {
		return right.b*a - right.a*b < 0;
	}
};

ll ft[16], rv[16], k,ans=0,lst[6];
pos g;
pair<pos, ll> n[16];

void src(pos cp,ll ind) {
	if (ind == k) {
		if (cp != g)return;
		ll v1 = 0,v2=1;
		for (int i = 0; i < k; i++) { v2 = (v2*rv[lst[i]]) % MOD; v1 += lst[i]; }
		v2 = (v2*ft[v1]) % MOD;
		ans += v2;
		return;
	}
	for (int i = 0; i <= n[ind].second; i++) {
		lst[ind] = i;
		pos np = mk(cp.first + i * n[ind].first.first, cp.second + i * n[ind].first.second);
		src(np, ind + 1);
	}
}


int main() {
	ft[0] = rv[0] = 1;
	for (int i = 1; i <= 15; i++) {
		ft[i] = (ft[i - 1] * i) % MOD;
		rv[i] = pw(ft[i], MOD - 2);
	}
	cin >> g.first >> g.second >> k;
	for (int i = 0; i < k; i++)cin >> n[i].first.first >> n[i].first.second >> n[i].second;
	src(mk(0, 0), 0);
	cout << ans << endl;
	return 0;
}