#include using namespace std; #define DEBUG(x) cerr<<#x<<": "< #define vl vector #define vii vector< vector > #define vll vector< vector > #define vs vector #define pii pair #define pis pair #define psi pair #define pll pair template pair operator+(const pair &s, const pair &t) { return pair(s.first + t.first, s.second + t.second); } template pair operator-(const pair &s, const pair &t) { return pair(s.first - t.first, s.second - t.second); } template ostream& operator<<(ostream& os, pair p) { os << "(" << p.first << ", " << p.second << ")"; return os; } #define X first #define Y second #define rep(i,n) for(int i=0;i<(int)(n);i++) #define rep1(i,n) for(int i=1;i<=(int)(n);i++) #define rrep(i,n) for(int i=(int)(n)-1;i>=0;i--) #define rrep1(i,n) for(int i=(int)(n);i>0;i--) #define REP(i,a,b) for(int i=a;i bool chmax(T &a, const T &b) { if (a bool chmin(T &a, const T &b) { if (a>b) { a = b; return 1; } return 0; } #define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end()); const ll inf = 1000000001; const ll INF = (ll)1e18 + 1; const long double pi = 3.1415926535897932384626433832795028841971L; #define Sp(p) cout<= 0; i--) { rfact[i] = (i + 1) * rfact[i + 1] % M; } } //http://drken1215.hatenablog.com/entry/2018/06/08/210000 //n���傫��fact���v�Z�ł��Ȃ��Ƃ��̂ق��̌v�Z���@�ɂ‚��ď����Ă��� ll nCr(ll n, ll r, ll M = MOD) { if (r > n) return 0; assert(fact[2] == 2); ll ret = fact[n]; if (rfact[r] == 0) { rfact[r] = mod_inverse(fact[r], M); } ret = (ret*rfact[r]) % M; if (rfact[n - r] == 0) { rfact[n - r] = mod_inverse(fact[n - r], M); } ret = (ret*rfact[n - r]) % M; return ret; } ll nHr(ll n, ll r) { return nCr(n+r-1, r); } template class LazySegmentTree { public: using F = function; // query_func using G = function; // update_func using H = function; // lazy to node (node, lazy, left, right) int n; vector node; vector lazy; T1 e1; T2 e2; F query_func; G update_func; H eval_func; LazySegmentTree(vector a, F query_func, G update_func, H eval_func, T1 e1, T2 e2) :query_func(query_func), update_func(update_func), eval_func(eval_func), e1(e1), e2(e2) { int _n = a.size(); n = 1; while (n < _n) n *= 2; node.resize(2 * n - 1, e1); lazy.resize(2 * n - 1, e2); for (int i = 0; i < _n; i++) node[i + n - 1] = a[i]; for (int i = n - 2; i >= 0; i--) { node[i] = query_func(node[i * 2 + 1], node[i * 2 + 2]); } } // k�Ԗڂ̃m�[�h�ɂ‚��Ēx���]�����s�� inline void eval(int k, int l, int r) { if (lazy[k] != e2) { // Change node[k] = eval_func(node[k], lazy[k], l, r); if (r - l > 1) { lazy[2 * k + 1] = update_func(lazy[2*k + 1], lazy[k]); lazy[2 * k + 2] = update_func(lazy[2*k + 2], lazy[k]); } lazy[k] = e2; // Change } } // [a, b)��x�ɂ��� void update(int a, int b, T2 x, int k, int l, int r) { // k �Ԗڂ̃m�[�h�ɑ΂��Ēx���]�����s�� eval(k, l, r); if (b <= l || r <= a) return; if (a <= l && r <= b) { lazy[k] = update_func(lazy[k], x); eval(k, l, r); } else { update(a, b, x, 2 * k + 1, l, (l + r) / 2); update(a, b, x, 2 * k + 2, (l + r) / 2, r); node[k] = query_func(node[2 * k + 1], node[2 * k + 2]); } } T1 query(int a, int b, int k, int l, int r) { eval(k, l, r); if (b <= l || r <= a) return e1; if (a <= l && r <= b) return node[k]; T1 resl = query(a, b, 2 * k + 1, l, (l + r) / 2); T1 resr = query(a, b, 2 * k + 2, (l + r) / 2, r); return query_func(resl, resr); } }; ll f(ll a, ll b) {return (a + b) % MOD;} ll g(ll a, ll b) {return a * b % MOD;} ll h(ll a, ll b, int l, int r) {return a * b % MOD;} signed main() { fio(); int n, m; cin >> n >> m; using P = pair; vector

lrp(m); vi non_zero(n + 1); int cnt = 0; rep (i, m) { int l, r, p; cin >> l >> r >> p; l--; lrp[i] = P(pii(l, r), p); if (p != 0) { non_zero[l]++; non_zero[r]--; cnt++; } } rep (i, n) { non_zero[i + 1] += non_zero[i]; } ll ans = 1; int temp = 0; rep (i, n) { if (non_zero[i] != 0) temp++; } ans = mod_pow(2, temp - cnt); // DEBUG(ans); vl dp(n + 1, 1); LazySegmentTree seg(dp, f, g, h, 0, 1); vector lr; rep (i, m) { if (lrp[i].second == 0) lr.push_back(lrp[i].first); } sort(all(lr), [](pii lr1, pii lr2) { return lr1.second < lr2.second; }); // DEBUG_VEC(lr); // DEBUG_VEC(non_zero); int al = 0; rep (i, lr.size()) { int l = lr[i].first, r = lr[i].second; for (int j = al; j < r; j++) { if (non_zero[j] != 0) { seg.update(j + 1, j + 2, 0, 0, 0, seg.n); continue; } // if (j < l) { // seg.update(j + 1, j + 2, 0, 0, 0, seg.n); // continue; // } ll wa = seg.query(0, j + 1, 0, 0, seg.n); seg.update(j + 1, j + 2, wa, 0, 0, seg.n); seg.update(0, j + 1, 2, 0, 0, seg.n); } seg.update(0, l + 1, 0, 0, 0, seg.n); al = r; } for (int j = al; j < n; j++) { if (non_zero[j] != 0) { seg.update(j + 1, j + 2, 0, 0, 0, seg.n); continue; } ll wa = seg.query(0, j + 1, 0, 0, seg.n); seg.update(j + 1, j + 2, wa, 0, 0, seg.n); seg.update(0, j + 1, 2, 0, 0, seg.n); } ll wa = seg.query(0, seg.n, 0, 0, seg.n); (ans *= wa) %= MOD; cout << ans << endl; } // vector fact(111111); // void solve() { // int n, m, k; // cin >> n >> m >> k; // double f = m, s = n - k + 1; // for (int i = k; i >= 1; i--) { // f *= (double)n / i; // s *= m; // if (f > s) break; // } // // double f = m * fact[n] / (fact[k] * fact[n - k]); // // double s = (n - k + 1) * pow(m, k); // // DEBUG(make_pair(f, s)); // if (f > s) cout << "Straight" << endl; // else cout << "Flush" << endl; // } // signed main() { // fio(); // fact[0] = 1; // rep (i, 111100) { // fact[i + 1] = fact[i] * (i + 1); // } // int q; // cin >> q; // while (q--) solve(); // }