#include<bits/stdc++.h>
#define IL inline
#define reg register
#define N 55
#define M (1<<10|5)
#define mod 998244353
IL int read()
{
    reg int x=0,f=0; reg char ch=getchar();
    while(ch<'0'||ch>'9')f|=ch=='-',ch=getchar();
    while(ch>='0'&&ch<='9')x=x*10+ch-'0',ch=getchar();
    return f?-x:x;
}

IL int Add(reg int x,reg int y){return x+y<mod?x+y:x+y-mod;}
IL void Pls(reg int &x,reg int y){x=Add(x,y);}
IL int Mul(reg int x,reg int y){long long r=1ll*x*y; return r<mod?r:r%mod;}
IL int power(reg int x,reg int p){reg int r=1; for(;p;p>>=1,x=Mul(x,x))if(p&1)r=Mul(r,x); return r;}

int n,m,q,mn[N];

IL void cmin(reg int &x,reg int y){x>y?x=y:0;}

int f[N][M],nf[N][M],con[N],binom[N][N],pop[M];
bool col[N];
int p[N],tot,cnt,full;
std::map<int,int>id;
std::vector<std::pair<int,int>>vec[N];

main()
{
    n=read(),m=read(),q=read();
    for(reg int i=1;i<=n;++i)mn[i]=n;
    for(reg int x,y,k;q--;)
    {
        x=read(),y=read(),k=read();
        cmin(mn[y],k),col[y]=1;
        if(!id.count(x))id[x]=++cnt;
        vec[y].push_back({id[x],k});
    }
    for(reg int i=1;i<=n;++i)if(col[i])p[tot++]=i;
    full=1<<tot;
    for(reg int s=1;s<full;++s)pop[s]=pop[s>>1]+(s&1);
    for(reg int i=0;i<=n;++i)con[i]=power(i,m-cnt);
    for(reg int i=0;i<=n;++i)binom[i][0]=1;
    for(reg int i=1,j;i<=n;++i)for(j=1;j<=i;++j)
        binom[i][j]=Add(binom[i-1][j],binom[i-1][j-1]);
    f[0][0]=1;
    for(reg int i=n,s,j,k,w,o;i;--i)
    {
        for(j=0;j<=n;++j)for(s=full;s--;)if(w=f[j][s])
        {
            reg int x=n-j,y=i-1;
            if(m>cnt)
            {
                if(x>=y)w=Mul(w,con[x-y]);
                else w=0;    
            }            
            static int val[N];
            for(k=1;k<=cnt;++k)val[k]=x-y;
            for(o=tot;o--;)if(~s>>o&1)
                for(auto &[row,t]:vec[p[o]])
                    if(t>i)--val[row];
            for(o=tot;o--;)if(~s>>o&1)
                for(auto &[row,t]:vec[p[o]])
                    if(t==i)val[row]=1;
            for(k=1;k<=cnt&&w;++k)
                if(val[k]>0)w=Mul(w,val[k]);
                else w=0;
            f[j][s]=w;
        }
        for(o=tot;o--;)if(mn[p[o]]>=i)for(s=full;s--;)if(~s>>o&1)
            for(j=0;j<=n;++j)if(w=f[j][s])Pls(f[j+1][s|(1<<o)],w);
        for(j=0;j<=n;++j)for(s=full;s--;)if(w=f[j][s])for(k=0;j+k<=n;++k)
            Pls(nf[j+k][s],Mul(w,binom[n-tot-j+pop[s]][k]));
        for(j=0;j<=n;++j)for(s=full;s--;)f[j][s]=nf[j][s],nf[j][s]=0;
    }
    printf("%d\n",f[n][full-1]);
}