#include <bits/stdc++.h>
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define F(i, x, y) for (int i = (x); i <= (y); i++)
#define R(i, x, y) for (int i = (x); i >= (y); i--)
#define FIO(FILE) freopen(FILE".in", "r", stdin), freopen(FILE".out", "w", stdout)

using namespace std;
typedef long long ll;
typedef pair<int, int> pi;
bool Mbe;

const int Q = 15;
const int N = 55;
const int T = (1 << 10) + 5;
const int P = 998244353;

int n, m, q, cx, cy, S;
int fc[N], ifc[N], mf[N], imf[N], pc[T], xid[N], mn[N];
int f[N][N][T], g[N][N][T], h[T];

vector<pi> t[N];
unordered_map<int, int> id;

int qpow(int p, int q) {
	int res = 1;
	for (; q; q >>= 1, p = 1ll * p * p % P) {
		if (q & 1) {
			res = 1ll * res * p % P;
		}
	}
	return res;
}

int gid(int y) {
	if (id.find(y) == id.end()) {
		return id[y] = ++cy;
	}
	return id[y];
}

int C(int n, int m) {
	if (n < m || m < 0) {
		return 0;
	}
	return 1ll * fc[n] * ifc[m] % P * ifc[n - m] % P;
}

void solve() {
	cin >> n >> m >> q;
	F (i, 1, q) {
		int x, y, w;
		cin >> y >> x >> w;
		t[x].eb(y, w);
	}
	F (i, 1, n) {
		if (t[i].empty()) {
			continue;
		}
		xid[i] = ++cx;
	}
	S = (1 << cx);
	F (i, 1, n) {
		if (t[i].empty()) {
			continue;
		}
		for (pi p : t[i]) {
			int y = p.fi, w = p.se;
			int idy = gid(y);
			F (j, 1, w) {
				F (s, 0, S - 1) {
					if ((s >> (xid[i] - 1)) & 1) {
						continue;
					}
					g[idy][j][s]++;
					if (!mn[xid[i]]) {
						mn[xid[i]] = w;
					} else {
						mn[xid[i]] = min(mn[xid[i]], w);
					}
				}
			}
		}
	}
	fc[0] = mf[0] = 1;
	F (i, 1, n) {
		fc[i] = 1ll * fc[i - 1] * i % P;
		mf[i] = qpow(fc[i], m - cy);
	}
	ifc[n] = qpow(fc[n], P - 2);
	imf[n] = qpow(ifc[n], m - cy);
	R (i, n - 1, 0) {
		ifc[i] = 1ll * ifc[i + 1] * (i + 1) % P;
		imf[i] = qpow(ifc[i], m - cy);
	}
	F (i, 1, S - 1) {
		pc[i] = __builtin_popcount(i);
	}
	f[n][0][0] = 1;
	R (i, n, 1) {
		F (j, 0, n - pc[S - 1]) {
			F (s, 0, S - 1) {
				f[i][j][s] = 1ll * f[i][j][s] * mf[n - i - j - pc[s] + 1] % P;
				F (t, 1, cy) {
					f[i][j][s] = 1ll * f[i][j][s] * fc[n - i - j - pc[s] - g[t][i][s] + 1] % P;
				}
			}
			F (k, j, n - pc[S - 1]) {
				int cf = C(k, j);
				F (s, 0, S - 1) {
					h[s] = f[i][j][s];
				}
				F (l, 0, cx - 1) {
					F (s, 0, S - 1) {
						if ((s >> l) & 1) {
							(h[s] += h[s ^ (1 << l)]) %= P;
						}
					}
				}
				F (t, 0, S - 1) {
					(f[i - 1][k][t] += 1ll * h[t] * cf % P) %= P;
				}
			}
		}
		F (k, 0, n - pc[S - 1]) {
			F (t, 0, S - 1) {
				int fl = 1;
				F (l, 0, cx - 1) {
					if (((t >> l) & 1) && mn[l + 1] < i) {
						fl = 0;
					}
				}
				if (!fl) {
					f[i - 1][k][t] = 0;
				} else {
					f[i - 1][k][t] = 1ll * f[i - 1][k][t] * imf[n - i - k - pc[t] + 1] % P;
					F (l, 1, cy) {
						f[i - 1][k][t] = 1ll * f[i - 1][k][t] * ifc[n - i - k - pc[t] - g[l][i][t] + 1] % P;
					}
				}
			}
		}
	}
	cout << f[0][n - pc[S - 1]][S - 1] << '\n';
}

bool Med;
int main() {
	// FIO("");
	ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	cerr << (&Mbe - &Med) / 1048576.0 << " MB\n";
	int T = 1;
	// cin >> T;
	while (T--) solve();
	cerr << (int)(1e3 * clock() / CLOCKS_PER_SEC) << " ms\n";
	return 0;
}