/// [Amberjack] CUT BEGIN
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;

typedef int _loop_int;
#define __GET_REP_MACRO(_1,_2,_3,NAME,...) NAME
#define __REP0(i,n) for(_loop_int i=0;i<(n);++i)
#define __REP1(i,a,b) for(_loop_int i=(a);i<(b);++i)
#define __REPR0(i,n) for(_loop_int i=(n)-1;i>=0;--i)
#define __REPR1(i,a,b) for(_loop_int i=(b)-1;i>=(a);--i)
#define REP(...) __GET_REP_MACRO(__VA_ARGS__,__REP1,__REP0)(__VA_ARGS__)
#define REPR(...) __GET_REP_MACRO(__VA_ARGS__,__REPR1,__REPR0)(__VA_ARGS__)

#ifdef BURI
#define __DEBUG0() "Hello"
#define __DEBUG1(x) #x"("<<(x)<<")"
#define __DEBUG2(x,...) #x"("<<(x)<<"), " __DEBUG1(__VA_ARGS__)
#define __DEBUG3(x,...) #x"("<<(x)<<"), " __DEBUG2(__VA_ARGS__)
#define __DEBUG4(x,...) #x"("<<(x)<<"), " __DEBUG3(__VA_ARGS__)
#define __DEBUG5(x,...) #x"("<<(x)<<"), " __DEBUG4(__VA_ARGS__)
#define __GET_DEBUG_MACRO(_1,_2,_3,_4,_5,NAME,...) NAME
#define __DEBUG(...) __GET_DEBUG_MACRO(__VA_ARGS__,__DEBUG5,__DEBUG4,__DEBUG3,__DEBUG2,__DEBUG1,__DEBUG0)(__VA_ARGS__)
#define DEBUG(...) cerr<<__DEBUG(__VA_ARGS__)<<endl
#else
#define DEBUG(...)
#endif

#define ALL(a) (a).begin(),(a).end() 
#define CHMIN(a,b) a=min((a),(b)) 
#define CHMAX(a,b) a=max((a),(b))

#define gc getchar_unlocked
inline void getll(ll &x){
  int sgn=1;x=0;
  char c=gc();
  while(c!='-'&&(c<'0'||c>'9'))c=gc();
  if(c=='-') sgn=-1; else x=c-'0';
  c=gc();
  while('0'<=c&&c<='9'){
    x*=10;
    x+=c-'0';
    c=gc();
  }
  x*=sgn;
}
inline void read(ll &x){getll(x);}
inline void read(int &x){ll y;getll(y);x=y;}
inline void read(float &x){scanf("%f",&x);}
inline void read(double &x){scanf("%lf",&x);}
inline void read(long double &x){scanf("%Lf",&x);}
inline void read(char *s){scanf("%s",s);}
// inline void read(char *s){char *t=s;char c;while((c=gc())==' '||c=='\n');while(c!=' '&&c!='\n'){*t++=c;c=gc();}}
inline void read(string &s){int len=s.size();char *buf=(char*)malloc(len*sizeof(char));scanf("%s",buf);s=string(buf);free(buf);}
inline void read(char &c){char *buf=(char*)malloc(5*sizeof(char));scanf("%s",buf);c=buf[0];free(buf);}
inline void read(){}
template<typename S,typename ...T>
inline void read(S& first, T&... rest){
  read(first);
  read(rest...);
}
/// [/Amberjack] CUT END


const int INF = 2125252830;
const int MAX = 100000;
 
int r,c,n;
int xy[2*MAX];
int val[MAX];
 
int xmin[MAX];
vector<pii> ys[MAX];
vector<pii> g[MAX];
ll dist[MAX];
bool used[MAX];
 
bool po[MAX];
int a;
int node[MAX];
int vere[MAX];
 
bool check(){
  REP(i,a)vere[node[i]] = i;
  REP(i,a)dist[i] = 0;
  REP(i,a)used[i] = false;
  dist[0] = 0;
  used[0] = true;
  queue<int> Q;
  Q.push(0);
  while(!Q.empty()){
    int p = Q.front(); Q.pop();
    int id = node[p];
    ll d = dist[p];
    REP(i,g[id].size()){
      int to = vere[g[id][i].first];
      ll cost = (ll)g[id][i].second;
      ll nd = d+cost;
      if(used[to]){
        if(dist[to]!=nd)return false;
      }else{
        dist[to] = nd;
        used[to] = true;
        Q.push(to);
      }
    }
  }
  // negative check
  ll sm = *min_element(dist,dist+a);
  REP(i,a){
    if(sm + (ll)xmin[node[i]] < 0){
      return false;
    }
    if(i==a-1)break;
    sm -= dist[i+1]-dist[i];
  }
  return true;
}
 
bool valid(int n){
  REP(i,n)po[i]=false;
  REP(i,n){
    if(po[i])continue;
    a = 0;
    po[i] = true;
    node[a++] = i;
    queue<int> Q;
    Q.push(i);
    while(!Q.empty()){
      int p = Q.front(); Q.pop();
      REP(j,g[p].size()){
        int to = g[p][j].first;
        if(po[to])continue;
        po[to] = true;
        node[a++] = to;
        Q.push(to);
      }
    }
    sort(node,node+a);
    if(!check())return false;
  }
  return true;
}
 
int Sx[MAX],Sy[MAX];
int Mx[MAX],My[MAX];
 
int main(){
  read(r,c,n);
  REP(i,n){
    read(xy[2*i],xy[2*i+1],val[i]);
    Sx[i] = xy[2*i];
    Sy[i] = xy[2*i+1];
  }
  sort(Sx,Sx+n);
  sort(Sy,Sy+n);
  r = unique(Sx,Sx+n)-Sx;
  c = unique(Sy,Sy+n)-Sy;
  REP(i,r)Mx[Sx[i]]=i;
  REP(i,c)My[Sy[i]]=i;
 
  REP(i,c)xmin[i] = INF;
  REP(i,n){
    int x,y;
    x=Mx[xy[2*i]];
    y=My[xy[2*i+1]];
    CHMIN(xmin[y],val[i]);
    ys[x].emplace_back(y,val[i]);
  }
  // graph
  REP(i,r){
    sort(ALL(ys[i]));
    vector<pii> &vec = ys[i];
    REP(j,vec.size()-1){
      int s,t;
      s = vec[j].first;
      t = vec[j+1].first;
      int sa = vec[j+1].second - vec[j].second;
      g[s].emplace_back(t,sa);
      g[t].emplace_back(s,-sa);
    }
  }
  if(!valid(r)){
    puts("No");
    return 0;
  }
  // ok
  puts("Yes");
  return 0;
}


Measured memory_bytes: 12544