#include<iostream>
#include<unordered_map>
#include<algorithm>
#include<vector>
typedef long long ll;
using namespace std;
struct Node
{
    ll l, r, c;
}node[100005];
Node e[200005];
int fa[300050];
int emptycnt = 2e5 + 5;
int cnt = 0;
int find(int x) {
    if (fa[x] != x)
        return fa[x] = find(fa[x]);
    return fa[x];
}
void merge(int x, int y) {
    int xx = find(x);
    int yy = find(y);
    if (xx != yy)
        fa[xx] = yy;
}
void init() {
    for (int i = 0; i <= 3e5+20; i++)
        fa[i] = i;
}
bool cmp(Node x, Node y) {
    if (x.c == y.c)
        return x.l < y.l;
    return x.c < y.c;
}
void No() {
    cout << "NO\n";
    exit(0);
}
int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    ll n, m;
    int k;
    cin >> n >> m >> k;
    unordered_map<ll, bool>mp;
    int tcnt = 0;
    for (int i = 1; i <= k; i++) {
        cin >> node[i].l >> node[i].r >> node[i].c;
        if (!mp[node[i].c]) {
            tcnt++;
            node[k + tcnt].l = n + 1;
            node[k + tcnt].r = n + 1;
            node[k + tcnt].c = node[i].c;
            mp[node[i].c] = 1;
        }
    }
    sort(node + 1, node + k + tcnt + 1, cmp);
    ll pre = 0;
    for (int i = 1; i <= k + tcnt; i++) {
        if (node[i].c != pre) {
            if (node[i].l > 1) {
                cnt++;
                e[cnt].l = 1;
                e[cnt].r = node[i].l - 1;
                e[cnt].c = node[i].c;
            }
            pre = node[i].c;
        }
        else {
            if (node[i].l > node[i - 1].r + 1) {
                cnt++;
                e[cnt].l = node[i - 1].r + 1;
                e[cnt].r = node[i].l - 1;
                e[cnt].c = node[i].c;
            }
        }
    }
    init();
    pre = 0;
    int p = 1, pe = 0;
    int lp = 1, op = 1;
    int len = 0;
    bool ok = 0;
    for (int i = 1; i <= cnt; i++) {
        if (e[i].c != pre) {
            p = lp;
            op = lp;
            lp = i;
            pe = i - 1;
            ok = 0;
            emptycnt++;
            if (e[i].c - pre > 2)
                No();
            else if (e[i].c - pre == 2) {
                ok = 1;
                if (e[i].r - e[i].l > 0)
                    No();
                if (find(i) == find(emptycnt))
                    No();
                merge(i, emptycnt);
            }
            else {
                while (p <= pe) {
                    if (e[p].r < e[i].l) {
                        p++;
                        continue;
                    }
                    else if (e[p].l > e[i].r)
                        break;
                    else {
                        ll temp = min(e[p].r, e[i].r) - max(e[p].l, e[i].l) + 1;
                        if (temp > 1)
                            No();
                        else {
                            if (find(p) == find(i))
                                No();
                            merge(p, i);
                        }
                    }
                    p++;
                }
            }
            pre = e[i].c;
        }
        else {
            if (ok) {
                if (e[i].r - e[i].l > 1)
                    No();
                if (find(i) == find(emptycnt))
                    No();
                merge(i, emptycnt);
            }
            else {
                p = max(op, p - 1);
                while (p <= pe) {
                    if (e[p].r < e[i].l) {
                        p++;
                        continue;
                    }
                    else if (e[p].l > e[i].r)
                        break;
                    else {
                        ll temp = min(e[p].r, e[i].r) - max(e[p].l, e[i].l) + 1;
                        if (temp > 1)
                            No();
                        else {
                            if (find(p) == find(i))
                                No();
                            merge(p, i);
                        }
                    }
                    p++;
                }
            }
        }
    }
    if (m - e[lp].c > 1)
        No();
    else if (m - e[lp].c == 1) {
        emptycnt++;
        for (int i = lp; i <= cnt; i++) {
            if (e[i].r - e[i].l > 0)
                No();
            if (find(i) == find(emptycnt))
                No();
            merge(i, emptycnt);
        }
    }
    cout << "YES\n";
    return 0;
}