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

#define endl '\n' 
// #define int long long
const int N = 2e6+5, mod = 1e9+7;

vector<pair<int,int>> c[N], v[N];
map<array<int,3>,int> mp;
int fa[N];

int find(int x) {
    while(x!=fa[x]) {
        x = fa[x] = fa[fa[x]];
    } return x;
}

void solve(){

    int n, m, k;
    cin>>n>>m>>k;
    for(int i=1;i<=N-5;i++) fa[i] = i;
    for(int i=1;i<=k;i++) {
        int l, r, y;
        cin>>l>>r>>y;
        if(y<=1e6) {
            c[y].push_back({l,r});
        }
    }
    if(m==1) {
        cout<<"YES"<<endl;
        return ;
    }
    if(m>=5*k) {
        cout<<"NO"<<endl;
        return ;
    }
    int cnt = 0;
    for(int i=1;i<=m&&i<=2*k+10;i++) {
        int l = 1;
        for(int j=0;j<c[i].size();j++) {
            if(l==n+1) break;
            int r = c[i][j].first-1;
            if(l<=r) {
                v[i].push_back({l,r});
                mp[{l,r,i}] = ++cnt;
            }
            l = c[i][j].second+1;
        }    
        if(l<=n) {
            v[i].push_back({l,n});
            mp[{l,n,i}] = ++cnt;
        }
    }
    auto ok = [&](int l, int r, int ll, int rr) {
        int len;
        int s = min(r, rr) - max(l, ll) + 1;
        len = max(0ll, s);
        return len>=2;
    };
    for(int i=2;i<=m;i++) {
        int len1 = v[i-1].size();
        int len2 = v[i].size();
        if(v[i-1].empty()) {
            continue;
        }
        else if(v[i].empty()) continue;
        for(int j=0;j<len1;j++) {
            for(int z=0;z<len2;z++) {
                auto [l,r] = v[i-1][j];
                auto [ll,rr] = v[i][z];
                if(ok(l,r,ll,rr)) {
                    cout<<"NO"<<endl;
                    return ;
                }
                else if(max(l,ll)<=min(r,rr)) {
                    int x = mp[{l,r,i-1}];
                    int y = mp[{ll,rr,i}];
                    int fx = find(x);
                    int fy = find(y);
                    if(fx==fy) {
                        cout<<"NO"<<endl;
                        return ;
                    }
                    fa[fx] = fy;
                }
            }
        }
    }
    cout<<"YES"<<endl;

}

int main() {

    ios::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);

    // int T;
    // cin>>T;
    // while(T--)
    solve();
}

answer.code: In lambda function:
answer.code:58:18: error: no matching function for call to ‘max(long long int, int&)’
   58 |         len = max(0ll, s);
      |               ~~~^~~~~~~~
In file included from /usr/include/c++/13/algorithm:60,
                 from /usr/include/x86_64-linux-gnu/c++/13/bits/stdc++.h:51,
                 from answer.code:1:
/usr/include/c++/13/bits/stl_algobase.h:257:5: note: candidate: ‘template<class _Tp> constexpr const _Tp& std::max(const _Tp&, const _Tp&)’
  257 |     max(const _Tp& __a, const _Tp& __b)
      |     ^~~
/usr/include/c++/13/bits/stl_algobase.h:257:5: note:   template argument deduction/substitution failed:
answer.code:58:18: note:   deduced conflicting types for parameter ‘const _Tp’ (‘long long int’ and ‘int’)
   58 |         len = max(0ll, s);
      |               ~~~^~~~~~~~
/usr/include/c++/13/bits/stl_algobase.h:303:5: note: candidate: ‘template<class _Tp, class _Compare> constexpr const _Tp& std::max(const _Tp&, const _Tp&, _Compare)’
  303 |     max(const _Tp& __a, const _Tp& __b, _Compare __comp)
      |     ^~~
/usr/include/c++/13/bits/stl_algobase.h:303:5: note:   template argument deduction/substitution failed:
answer.code:58:18: note:   deduced conflicting types for parameter ‘const _Tp’ (‘long long int’ and ‘int’)
   58 |         len = max(0ll, s);
      |               ~~~^~~~~~~~
In file included from /usr/include/c++/13/algorithm:61:
/usr/include/c++/13/bits/stl_algo.h:5795:5: note: candidate: ‘template<class _Tp> constexpr _Tp std::max(initializer_list<_Tp>)’
 5795 |     max(initializer_list<_Tp> __l)
      |     ^~~
/usr/include/c++/13/bits/stl_algo.h:5795:5: note:   template argument deduction/substitution failed:
answer.code:58:18: note:   mismatched types ‘std::initializer_list<_Tp>’ and ‘long long int’
   58 |         len = max(0ll, s);
      |               ~~~^~~~~~~~
/usr/include/c++/13/bits/stl_algo.h:5805:5: note: candidate: ‘template<class _Tp, class _Compare> constexpr _Tp std::max(initializer_list<_Tp>, _Compare)’
 5805 |     max(initializer_list<_Tp> __l, _Compare __comp)
      |     ^~~
/usr/include/c++/13/bits/stl_algo.h:5805:5: note:   template argument deduction/substitution failed:
answer.code:58:18: note:   mismatched types ‘std::initializer_list<_Tp>’ and ‘long long int’
   58 |         len = max(0ll, s);
      |               ~~~^~~~~~~~