#include #include #include template struct LazySegmentTree { TLAZY zero_lazy; TRET zero_ret; int N; int head; std::vector data; std::vector lazy; // Here, you have to calculate data[pos] from children (data[l], data[r]), // Assumptions: `lazy[pos] = lazy[l] = lazy[r] = zero_lazy` virtual void merge_data(int pos) = 0; // Here, you must propagate lazy[pos] and update data[pos] by reflecting lazy[pos], without inconsistency // After this, lazy[pos] must be zero_lazy. virtual void reflect_lazy(int pos) = 0; // operate d to lazy[pos] (merge two TLAZY's) virtual void overlap_lazy(int pos, const TLAZY &d) = 0; // Assumption: `lazy[pos] = zero_lazy` virtual TRET data2ret(int pos, const TQUERY &query) = 0; virtual TRET merge_ret(const TRET &l, const TRET &r, const TQUERY &query) = 0; ////// general description ////// LazySegmentTree() = default; void initialize(const std::vector &data_init, const TDATA &zero_data, const TLAZY &zero_lazy_, const TRET &zero_ret_) { N = data_init.size(); head = 1; while (head < N) head <<= 1; zero_lazy = zero_lazy_; zero_ret = zero_ret_; data.assign(head * 2, zero_data); lazy.assign(head * 2, zero_lazy); std::copy(data_init.begin(), data_init.end(), data.begin() + head); for (int pos = head; --pos;) merge_data(pos); } void _update(int begin, int end, const TLAZY &delay, int pos, int l, int r) { // Operate `delay` to the node pos // After this, lazy[pos] MUST be zero so that merge_data() works correctly if (begin <= l and r <= end) { // Update whole [l, r) by delay overlap_lazy(pos, delay); reflect_lazy(pos); } else if (begin < r and l < end) { // Update somewhere in [l, r) reflect_lazy(pos); _update(begin, end, delay, pos * 2, l, (l + r) / 2); _update(begin, end, delay, pos * 2 + 1, (l + r) / 2, r); merge_data(pos); } else reflect_lazy(pos); } void update(int begin, int end, const TLAZY &delay) { _update(begin, end, delay, 1, 0, head); } TRET _get(int begin, int end, int pos, int l, int r, const TQUERY &query) // Get value in [begin, end) { reflect_lazy(pos); if (begin <= l and r <= end) return data2ret(pos, query); else if (begin < r and l < end) { TRET vl = _get(begin, end, pos * 2, l, (l + r) / 2, query); TRET vr = _get(begin, end, pos * 2 + 1, (l + r) / 2, r, query); return merge_ret(vl, vr, query); } else return zero_ret; } TRET get(int begin, int end, const TQUERY &query) { return _get(begin, end, 1, 0, head, query); } }; template struct RangeUpdateRangeSum : public LazySegmentTree, std::pair, T, std::tuple<>> { using TDATA = std::pair; using TLAZY = std::pair; using Empty = std::tuple<>; using SegTree = LazySegmentTree; using SegTree::data; using SegTree::lazy; void merge_data(int i) override { data[i] = std::make_pair(data[i * 2].first + data[i * 2 + 1].first, data[i * 2].second + data[i * 2 + 1].second); }; void reflect_lazy(int i) override { if (lazy[i].second) { if (i < SegTree::head) overlap_lazy(i * 2, lazy[i]), overlap_lazy(i * 2 + 1, lazy[i]); data[i].first = lazy[i].first * data[i].second; } lazy[i].second = false; } void overlap_lazy(int i, const TLAZY &p) override { if (p.second) lazy[i] = p; } T data2ret(int i, const Empty &) override { return data[i].first; } T merge_ret(const T &l, const T &r, const Empty &) override { return l + r; } void update(int l, int r, T val) { SegTree::update(l, r, TLAZY(val, true)); } T get(int l, int r) { return SegTree::get(l, r, {}); } RangeUpdateRangeSum(const std::vector &seq) : SegTree::LazySegmentTree() { std::vector vec; std::transform(seq.begin(), seq.end(), std::back_inserter(vec), [](T x){ return TDATA(x, 1); }); // for (const auto &x : seq) vec.emplace_back(x, 1); SegTree::initialize(vec, TDATA(0, 0), TLAZY(0, false), 0); } }; #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector &vec, int len) { vec.resize(len); } template void ndarray(vector &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); } template void ndfill(V &x, const T &val) { x = val; } template void ndfill(vector &vec, const T &val) { for (auto &v : vec) ndfill(v, val); } template bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; } template bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector srtunq(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL #define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl #else #define dbg(x) #endif template struct ModInt { using lint = long long; int val; constexpr ModInt() : val(0) {} constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; } constexpr ModInt(lint v) { _setval(v % mod + mod); } explicit operator bool() const { return val != 0; } constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); } constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); } constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); } constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); } constexpr ModInt operator-() const { return ModInt()._setval(mod - val); } constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; } constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; } constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; } constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); } friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); } friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); } friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); } constexpr bool operator==(const ModInt &x) const { return val == x.val; } constexpr bool operator!=(const ModInt &x) const { return val != x.val; } bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; } friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; } constexpr lint power(lint n) const { lint ans = 1, tmp = this->val; while (n) { if (n & 1) ans = ans * tmp % mod; tmp = tmp * tmp % mod; n /= 2; } return ans; } constexpr lint inv() const { return this->power(mod - 2); } constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); } constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; } inline ModInt fac() const { static std::vector facs; int l0 = facs.size(); if (l0 > this->val) return facs[this->val]; facs.resize(this->val + 1); for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i)); return facs[this->val]; } ModInt doublefac() const { lint k = (this->val + 1) / 2; if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac(); else return ModInt(k).fac() * ModInt(2).power(k); } ModInt nCr(const ModInt &r) const { if (this->val < r.val) return ModInt(0); return this->fac() / ((*this - r).fac() * r.fac()); } }; using mint = ModInt<1000000007>; int main() { int N, M; cin >> N >> M; vector r2lp(N + 1, pint(-1, -1)); vector v(N + 1, 0); v[0] = mint(2).power(N); RangeUpdateRangeSum segtree(v); while (M--) { int l, r, p; cin >> l >> r >> p; r2lp[r] = make_pair(l, p); } mint inv2 = mint(2).inv(); int cnt = 0; FOR(r, 1, N + 1) { auto [l, p] = r2lp[r]; if (l == -1) { segtree.update(r, r + 1, segtree.get(0, r) * inv2); continue; } if (p == 0) { segtree.update(r, r + 1, segtree.get(0, r) * inv2); segtree.update(0, l, 0); } else { segtree.update(l, r, 0); cnt++; } } cout << segtree.get(0, N + 1) / mint(2).power(cnt) << '\n'; }