#include <bits/stdc++.h>
#define int long long 
using namespace std;
const int INF=1e6+5;
const int Mod=998244353;
const int INFN=55;
const int INFS=1035;
struct P3{
    int x,y,z;
}aa[INF];
int n,m,q,b[INF],c[INF],sum3,ans,bb[INF],L;
int fav[INF],ifav[INF];
int ksm(int x,int y) {
    int ba=x%Mod,ans=1;
    while (y) {
        if (y&1) ans=(ans*ba)%Mod;
        ba=(ba*ba)%Mod;y>>=1;
    } 
    return ans;
}
void init() {
	fav[0]=1;int N=1e6;
	for (int i=1;i<=N;i++) fav[i]=fav[i-1]*i%Mod;
	ifav[N]=ksm(fav[N],Mod-2);
	for (int i=N-1;~i;i--) ifav[i]=ifav[i+1]*(i+1)%Mod;
}
int C(int x,int y) {
	if (x<y) return 0;
	return fav[x]*ifav[y]%Mod*ifav[x-y]%Mod;
}
int vis6[INFN],L6[INFN],B[INFN][INFN];
int tot3,num[INFN][INFN],s5[INFN],S5[INFS],num2[INFN][INFN],sum4i[INFN][INFN],sum4[INFN][INFN],len[INFN];
int f[INFN][INFN][INFS],vis0[INFN][INFS],sum5[INFN][13][INFN],sum5i[INFN][13][INFN];
int C6[INFN*2][INFN*2];
signed main()
{
    ios::sync_with_stdio(false);
    cin>>n>>m>>q;init();
    C6[0][0]=1;
    for (int i=1;i<=100;i++) {
    	C6[i][0]=C6[i][i]=1;
    	for (int j=1;j<i;j++)
    		C6[i][j]=C6[i-1][j-1]+C6[i-1][j],C6[i][j]%=Mod;
	}
    for (int i=1;i<=q;i++) 
        cin>>aa[i].x>>aa[i].y>>aa[i].z,vis6[aa[i].y]=1;
	int sum6=0;
	for (int w=1;w<=n;w++) 
		if (vis6[w]) sum6+=vis6[w],L6[++L6[0]]=w,L+=vis6[w];
    sort(aa+1,aa+1+q,[](P3 xx,P3 yy){return xx.x<yy.x;});
	for (int i=1;i<=q;i++) {
		int r=i;
		while (r+1<=q && aa[r+1].x==aa[r].x) r++;
		++tot3;
		for (int w=i;w<=r;w++) {
			num[tot3][aa[w].y]=aa[w].z,len[tot3]++;
//			cerr<<num[tot3][aa[w].y]<<" "<<tot3<<" "<<aa[w].y<<" QAQWQ?\n";
			for (int t=1;t<=L6[0];t++)
				if (L6[t]==aa[w].y) s5[tot3]|=(1ll<<(t-1));
		}
		for (int w=i;w<=r;w++) 
			for (int q=aa[w].z;q;q--) 
				num2[tot3][q]++;
		i=r;
	}
    sum3=0;
    for (int i=1;i<=q;i++) {
        if (aa[i].x!=aa[i-1].x) sum3++;
	}
	for (int i=0;i<=n;i++) {
		sum4[i][n+1]=1;
		for (int l=n;l;l--)
			sum4[i][l]=sum4[i][l+1]*ksm(l-(i+1)+1,m-sum3),sum4[i][l]%=Mod;
		for (int l=1;l<=n+1;l++)
			sum4i[i][l]=ksm(sum4[i][l],Mod-2);
		// for (int l=1;l<=n;l++) {
		// 	for (int r=l;r<=n;r++) {
		// 		if (l==r) sum4[i][l][r]=ksm(l-(i+1)+1,m-sum3);
		// 		else sum4[i][l][r]=sum4[i][l][r-1]*ksm(r-(i+1)+1,m-sum3)%Mod;
		// 	}
		// }
	}
	for (int i=0;i<n;i++) {
		S5[i]=(1<<n)-1;
		for (int t=0;t<(1<<L);t++) {
			for (int u=0;u<L6[0];u++)
				if ((t>>u)&1) {
					for (int w=1;w<=tot3;w++) { 
						if (!((s5[w]>>u)&1)) continue;
						// num[w][L6[u+1]]
						if (num[w][L6[u+1]]<i+1) {
							vis0[i][t]=1;
							S5[i]&=~(1<<u);
						}
					}
				}
		}
	}
	for (int i=0;i<=n;i++) {
		for (int u=1;u<=tot3;u++) {
			// for (int l=1;l<=n;l++) {
			// 	for (int r=l;r<=n;r++) {
			// 		if (l==r) sum5[i][u][l][r]=(r+len[u]-(i+1)+1-num2[u][i+1]);
			// 		else sum5[i][u][l][r]=sum5[i][u][l][r-1]*(r+len[u]-(i+1)+1-num2[u][i+1])%Mod;
			// 	}
			// }
			sum5[i][u][n+1]=(n+1+len[u]-(i+1)+1-num2[u][i+1]);
			for (int l=n;l;l--) 
				sum5[i][u][l]=sum5[i][u][l+1]*(l+len[u]-(i+1)+1-num2[u][i+1])%Mod;
			for (int l=1;l<=n+1;l++)
				sum5i[i][u][l]=ksm(sum5[i][u][l],Mod-2);
			
		}
	}
	f[0][0][0]=1;
	for (int i=0;i<n;i++) {
		for (int j=0;j<=n-L;j++) {
			for (int s=0;s<(1<<L);s++) {
				if (!f[i][j][s]) continue;
				// 钦定填了 k 列，t 集合列
				for (int k=0;k<=n-L-j;k++) {
					int S=((1<<L)-s-1)&S5[i];
					int ba=C6[n-L-j][k];
					int P2=__builtin_popcount(s);
					ba*=sum4[i][j+P2+1];ba%=Mod;
					for (int u=1;u<=tot3;u++) {
						int l=j+__builtin_popcount(s&(~s5[u]))+1;
						ba*=sum5[i][u][l],ba%=Mod;
					}
					f[i+1][j+k][s]+=f[i][j][s]*ba;f[i+1][j+k][s]%=Mod;
					// for (int t=S;;t=(t-1)&S) {
					// 	int ba=C6[n-L-j][k],P=__builtin_popcount(t);
					// 	int P2=__builtin_popcount(s);
					// 	ba*=sum4[i][j+P2+1]*sum4i[i][j+P2+k+P+1]%Mod,ba%=Mod;
					// 	if (!ba) {if (!t) break;continue;}
					// 	for (int u=1;u<=tot3;u++) {
					// 		int l=j+__builtin_popcount(s&(~s5[u]))+1,r=j+__builtin_popcount((s+t)&(~s5[u]))+k;
					// 		ba*=sum5[i][u][l]*sum5i[i][u][r+1]%Mod,ba%=Mod;
					// 	}
					// 	if (!ba) {if (!t) break;continue;}
					// 	f[i+1][j+k][s+t]+=f[i][j][s]*ba;
					// 	f[i+1][j+k][s+t]%=Mod;
					// 	if (!t) break;
					// }
				}
			}
		}
		for (int j=0;j<=n-L;j++) {
			for (int p=0;p<L;p++) {
				if ((S5[i]>>p)&1) {
					for (int s=0;s<(1<<L);s++)
						if ((s>>p)&1) 
							f[i+1][j][s]+=f[i+1][j][s^(1<<p)],f[i+1][j][s]%=Mod;
				}
			}
		}
		for (int j=0;j<=n-L;j++) 
			for (int s=0;s<(1<<L);s++) {
				int P=__builtin_popcount(s);
				f[i+1][j][s]*=sum4i[i][j+P+1];f[i+1][j][s]%=Mod;
				for (int u=1;u<=tot3;u++) {
					int r=j+__builtin_popcount(s&(~s5[u]));
					f[i+1][j][s]*=sum5i[i][u][r+1]%Mod,f[i+1][j][s]%=Mod;
				}
			}
	}
    cout<<f[n][n-L][(1<<L)-1]<<"\n";
    return 0;
}