import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";

	public static void main(String[] args) throws Exception {
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);

		solver();
		out.flush();
	}

	static long nl() {
		try {
			long num = 0;
			boolean minus = false;
			while ((num = is.read()) != -1 && !((num >= '0' && num <= '9') || num == '-'))
				;
			if (num == '-') {
				num = 0;
				minus = true;
			} else {
				num -= '0';
			}

			while (true) {
				int b = is.read();
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
			}
		} catch (IOException e) {
		}
		return -1;
	}

	static char nc() {
		try {
			int b = skip();
			if (b == -1)
				return 0;
			return (char) b;
		} catch (IOException e) {
		}
		return 0;
	}

	static double nd() {
		try {
			return Double.parseDouble(ns());
		} catch (Exception e) {
		}
		return 0;
	}

	static String ns() {
		try {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			if (b == -1)
				return "";
			sb.append((char) b);
			while (true) {
				b = is.read();
				if (b == -1)
					return sb.toString();
				if (b <= ' ')
					return sb.toString();
				sb.append((char) b);
			}
		} catch (IOException e) {
		}
		return "";
	}

	public static char[] ns(int n) {
		char[] buf = new char[n];
		try {
			int b = skip(), p = 0;
			if (b == -1)
				return null;
			buf[p++] = (char) b;
			while (p < n) {
				b = is.read();
				if (b == -1 || b <= ' ')
					break;
				buf[p++] = (char) b;
			}
			return Arrays.copyOf(buf, p);
		} catch (IOException e) {
		}
		return null;
	}

	public static byte[] nse(int n) {
		byte[] buf = new byte[n];
		try {
			int b = skip();
			if (b == -1)
				return null;
			is.read(buf);
			return buf;
		} catch (IOException e) {
		}
		return null;
	}

	static int skip() throws IOException {
		int b;
		while ((b = is.read()) != -1 && !(b >= 33 && b <= 126))
			;
		return b;
	}

	static boolean eof() {
		try {
			is.mark(1000);
			int b = skip();
			is.reset();
			return b == -1;
		} catch (IOException e) {
			return true;
		}
	}

	static int ni() {
		try {
			int num = 0;
			boolean minus = false;
			while ((num = is.read()) != -1 && !((num >= '0' && num <= '9') || num == '-'))
				;
			if (num == '-') {
				num = 0;
				minus = true;
			} else {
				num -= '0';
			}

			while (true) {
				int b = is.read();
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
			}
		} catch (IOException e) {
		}
		return -1;
	}

	static long MOD = 1_000_000_000 + 7;

	static void solver() {
		int gx = ni();
		int gy = ni();
		int k = ni();// the number of kinds of crystals

		if (Math.abs(gx) > 100000)
			throw new AssertionError();
		if (k <= 0 || k > 5)
			throw new AssertionError();

		P np = new P(-1, -1);
		P[] ps = new P[1 << (4 * k)];
		for (int i = 1; i < ps.length; i++) {
			ps[i] = np;
		}
		ps[0] = new P(0, 0);

		for (int i = 0; i < k; i++) {
			int x = ni();
			int y = ni();
			P v = new P(x, y);
			int n = ni();
			if (Math.abs(x) > 10000 || Math.abs(y) > 10000)
				throw new AssertionError();
			if (n <= 0 || n > 15)
				throw new AssertionError();

			for (int j = 0; n > 0; j++) {
				int mul = Math.min(1 << j, n);
				n -= mul;
				P u = v.multiply(mul);
				for (int l = (1 << (4 * i + j)) - 1; l >= 0; l--) {
					if (ps[l] == np)
						continue;
					ps[l + (mul << (4 * i))] = ps[l].add(u);
				}
			}
		}
		long ans = 0;
		for (int i = 0; i < (1 << (4 * k)); i++) {
			if (ps[i] == np)
				continue;
			if (ps[i].x != gx || ps[i].y != gy)
				continue;
			int s = i;
			long total = 0;
			long denomi = 1;
			for (; s > 0; s >>= 4) {
				int d = s & 15;
				total += d;
				denomi = denomi * inv(fact(d), MOD) % MOD;
			}
			ans = (ans + fact(total) * denomi) % MOD;
		}
		out.println(ans);
	}

	static class P {
		int x;
		int y;

		P(int x, int y) {
			this.x = x;
			this.y = y;
		}

		P multiply(int m) {
			return new P(x * m, y * m);
		}

		P add(P p) {
			return new P(x + p.x, y + p.y);
		}
	}

	static long fact(long nume) {
		long ans = 1;
		for (int i = 1; i <= nume; i++) {
			ans *= i;
			ans %= MOD;
		}
		return ans;
	}

	static long inv(long a, long mod) {
		a = a % mod;
		long b = mod;
		long p = 1, q = 0;

		while (b > 1) {
			long c = b / a;
			b = b % a;
			q = q - p * c;
			long d = b;
			b = a;
			a = d;
			d = p;
			p = q;
			q = d;
		}
		while (q < 0)
			q += mod;
		return q;
	}
}