//start of jonathanirvings' template v3.0.3 (BETA)

#include <bits/stdc++.h>
using namespace std;

typedef long long LL;
typedef pair<int,int> pii;
typedef pair<LL,LL> pll;
typedef pair<string,string> pss;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<pii> vii;
typedef vector<LL> vl;
typedef vector<vl> vvl;

double EPS = 1e-9;
int INF = 1000000005;
long long INFF = 1000000000000000005LL;
double PI = acos(-1);
int dirx[8] = {-1,0,0,1,-1,-1,1,1};
int diry[8] = {0,1,-1,0,-1,1,-1,1};

#ifdef TESTING
  #define DEBUG fprintf(stderr,"====TESTING====\n")
  #define VALUE(x) cerr << "The value of " << #x << " is " << x << endl
  #define debug(...) fprintf(stderr, __VA_ARGS__)
#else
  #define DEBUG 
  #define VALUE(x)
  #define debug(...)
#endif

#define FOR(a,b,c) for (int (a)=(b);(a)<(c);++(a))
#define FORN(a,b,c) for (int (a)=(b);(a)<=(c);++(a))
#define FORD(a,b,c) for (int (a)=(b);(a)>=(c);--(a))
#define FORSQ(a,b,c) for (int (a)=(b);(a)*(a)<=(c);++(a))
#define FORC(a,b,c) for (char (a)=(b);(a)<=(c);++(a))
#define FOREACH(a,b) for (auto &(a) : (b))
#define REP(i,n) FOR(i,0,n)
#define REPN(i,n) FORN(i,1,n)
#define MAX(a,b) a = max(a,b)
#define MIN(a,b) a = min(a,b)
#define SQR(x) ((LL)(x) * (x))
#define RESET(a,b) memset(a,b,sizeof(a))
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define ALL(v) v.begin(),v.end()
#define ALLA(arr,sz) arr,arr+sz
#define SIZE(v) (int)v.size()
#define SORT(v) sort(ALL(v))
#define REVERSE(v) reverse(ALL(v))
#define SORTA(arr,sz) sort(ALLA(arr,sz))
#define REVERSEA(arr,sz) reverse(ALLA(arr,sz))
#define PERMUTE next_permutation
#define TC(t) while(t--)

inline string IntToString(LL a){
  char x[100];
  sprintf(x,"%lld",a); string s = x;
  return s;
}

inline LL StringToInt(string a){
  char x[100]; LL res;
  strcpy(x,a.c_str()); sscanf(x,"%lld",&res);
  return res;
}

inline string GetString(void){
  char x[1000005];
  scanf("%s",x); string s = x;
  return s;
}

inline string uppercase(string s){
  int n = SIZE(s); 
  REP(i,n) if (s[i] >= 'a' && s[i] <= 'z') s[i] = s[i] - 'a' + 'A';
  return s;
}

inline string lowercase(string s){
  int n = SIZE(s); 
  REP(i,n) if (s[i] >= 'A' && s[i] <= 'Z') s[i] = s[i] - 'A' + 'a';
  return s;
}

inline void OPEN (string s) {
  freopen ((s + ".in").c_str (), "r", stdin);
  freopen ((s + ".out").c_str (), "w", stdout);
}

//end of jonathanirvings' template v3.0.3 (BETA)

int r,c,n;
pii pos[100005];
int isi[100005];
vi adax[100005];
int miny[100005];
vii maju[100005];
int root[100005];
LL sum[100005];
LL minn[100005];
LL minnn;

bool f(int a,int b)
{
  return pos[a].se < pos[b].se;
}

void dfs(int pt,int now,LL cur)
{
  root[now] = pt;
  sum[now] = cur;
  MIN(minnn,cur);
  REP(i,SIZE(maju[now])) if (root[maju[now][i].fi] == -1)
  {
    dfs(pt,maju[now][i].fi,cur + maju[now][i].se);
  }
}

int main()
{
  scanf("%d %d",&r,&c);
  scanf("%d",&n);
  FORN(j,1,c) miny[j] = INF;
  REP(i,n)
  {
    scanf("%d %d %d",&pos[i].fi,&pos[i].se,&isi[i]);
    adax[pos[i].fi].pb(i);
    MIN(miny[pos[i].se],isi[i]);
  }
  FORN(i,1,r) sort(ALL(adax[i]),f);
  FORN(tries,1,1)
  {
    FORN(i,1,r)
    {
      /*int minn = INF;
      REP(j,SIZE(adax[i]))
      {
        MIN(minn,isi[adax[i][j]]);
      }
      REP(j,SIZE(adax[i]))
      {
        int y = pos[adax[i][j]].se;
        if (minn - isi[adax[i][j]] + miny[y] < 0)
        {
          puts("No");
          return 0;
        }
      }*/
      FOR(j,1,SIZE(adax[i]))
      {
        int ixa = adax[i][j-1];
        int ixb = adax[i][j];
        maju[pos[ixa].se].pb(mp(pos[ixb].se,isi[ixb] - isi[ixa]));
        maju[pos[ixb].se].pb(mp(pos[ixa].se,isi[ixa] - isi[ixb]));
      }
    }
    RESET(root,-1);
    FORN(j,1,c) if (root[j] == -1)
    {
      minnn = INFF;
      dfs(j,j,0);
      minn[j] = minnn;
    }
    FORN(i,1,r)
    {
      FOR(j,1,SIZE(adax[i]))
      {
        int ixa = adax[i][j-1];
        int ixb = adax[i][j];
        int ya = pos[ixa].se;
        int yb = pos[ixb].se;
        if (isi[ixb] - isi[ixa] != sum[yb] - sum[ya])
        {
          puts("No");
          return 0;
        }
      }
      REP(j,SIZE(adax[i]))
      {
        int ix = adax[i][j];
        int y = pos[ix].se;
        if (isi[ix] - sum[y] + minn[root[y]] < 0)
        {
          puts("No");
          return 0;
        }
      }
    }
    /*REPN(i,r) adax[i].clear();
    REPN(j,c) aday[j].clear();
    swap(r,c);
    REP(i,n)
    {
      swap(pos[i].fi,pos[i].se);
      adax[pos[i].fi].pb(i);
      aday[pos[i].se].insert(i);
    }*/
  }
  puts("Yes");
  return 0;
}










Measured memory_bytes: 14720