#line 1 "main.cpp" #include #line 2 "/home/user/Library/utils/macros.hpp" #define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i)) #define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i)) #define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i)) #define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i)) #define ALL(x) std::begin(x), std::end(x) #line 4 "/home/user/Library/modulus/modpow.hpp" inline int32_t modpow(uint_fast64_t x, uint64_t k, int32_t MOD) { assert (/* 0 <= x and */ x < (uint_fast64_t)MOD); uint_fast64_t y = 1; for (; k; k >>= 1) { if (k & 1) (y *= x) %= MOD; (x *= x) %= MOD; } assert (/* 0 <= y and */ y < (uint_fast64_t)MOD); return y; } #line 5 "/home/user/Library/modulus/modinv.hpp" inline int32_t modinv_nocheck(int32_t value, int32_t MOD) { assert (0 <= value and value < MOD); if (value == 0) return -1; int64_t a = value, b = MOD; int64_t x = 0, y = 1; for (int64_t u = 1, v = 0; a; ) { int64_t q = b / a; x -= q * u; std::swap(x, u); y -= q * v; std::swap(y, v); b -= q * a; std::swap(b, a); } if (not (value * x + MOD * y == b and b == 1)) return -1; if (x < 0) x += MOD; assert (0 <= x and x < MOD); return x; } inline int32_t modinv(int32_t x, int32_t MOD) { int32_t y = modinv_nocheck(x, MOD); assert (y != -1); return y; } #line 6 "/home/user/Library/modulus/mint.hpp" /** * @brief quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$ */ template struct mint { int32_t value; mint() : value() {} mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {} mint(int32_t value_, std::nullptr_t) : value(value_) {} explicit operator bool() const { return value; } inline mint operator + (mint other) const { return mint(*this) += other; } inline mint operator - (mint other) const { return mint(*this) -= other; } inline mint operator * (mint other) const { return mint(*this) *= other; } inline mint & operator += (mint other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; } inline mint & operator -= (mint other) { this->value -= other.value; if (this->value < 0) this->value += MOD; return *this; } inline mint & operator *= (mint other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; } inline mint operator - () const { return mint(this->value ? MOD - this->value : 0, nullptr); } inline bool operator == (mint other) const { return value == other.value; } inline bool operator != (mint other) const { return value != other.value; } inline mint pow(uint64_t k) const { return mint(modpow(value, k, MOD), nullptr); } inline mint inv() const { return mint(modinv(value, MOD), nullptr); } inline mint operator / (mint other) const { return *this * other.inv(); } inline mint & operator /= (mint other) { return *this *= other.inv(); } }; template mint operator + (int64_t value, mint n) { return mint(value) + n; } template mint operator - (int64_t value, mint n) { return mint(value) - n; } template mint operator * (int64_t value, mint n) { return mint(value) * n; } template mint operator / (int64_t value, mint n) { return mint(value) / n; } template std::istream & operator >> (std::istream & in, mint & n) { int64_t value; in >> value; n = value; return in; } template std::ostream & operator << (std::ostream & out, mint n) { return out << n.value; } #line 4 "main.cpp" using namespace std; constexpr int64_t MOD = 1000000007; mint solve_zero(int n, int m, const vector& l, const vector& r) { if (m < 10) { cerr << "zero" << endl; cerr << "n = " << n << endl; cerr << "m = " << m << endl; REP (i, m) { cerr << "[" << l[i] << ", " << r[i] << ")" << endl; } } vector event(n + 1, -1); REP (j, m) { event[r[j]] = l[j]; } vector > dp(n + 2); dp[0] = 1; int j = 0; REP (i, n + 1) { j = max(j, event[i] + 1); REP3 (k, j, i + 1) { dp[i + 1] += mint(2).pow(i - k) * dp[k]; } } if (m < 10) { cerr << "ans = " << dp[n + 1] << endl; } return dp[n + 1]; } mint solve_nonzero(int n, int m, const vector& l, const vector& r, const vector& p) { if (m < 10) { cerr << "nonzero" << endl; cerr << "n = " << n << endl; cerr << "m = " << m << endl; REP (i, m) { cerr << "[" << l[i] << ", " << r[i] << ") " << p[i] << endl; } } return mint(2).pow(n - m); } mint solve(int n, int m, const vector& l, const vector& r, const vector& p) { // [l, r) // list events vector > event_l(n + 1); vector event_r(n + 1, -1); REP (j, m) { event_l[l[j]].push_back(j); event_r[r[j]] = j; } // split queries int n0 = 0; int m0 = 0; vector l0, r0; int n1 = 0; int m1 = 0; vector l1, r1, p1; vector table(m, -1); int cnt = 0; REP (i, n + 1) { for (int j : event_l[i]) { if (p[j] == 0) { int k = m0; table[j] = k; ++ m0; l0.push_back(n0); r0.push_back(-1); } else { int k = m1; table[j] = k; ++ m1; l1.push_back(n1); r1.push_back(-1); p1.push_back(p[j]); ++ cnt; } } if (event_r[i] != -1) { int j = event_r[i]; int k = table[j]; if (p[j] == 0) { r0[k] = n0; } else { r1[k] = n1; -- cnt; } } if (i < n) { if (cnt) { ++ n1; } else { ++ n0; } } } return solve_zero(n0, m0, l0, r0) * solve_nonzero(n1, m1, l1, r1, p1); } // generated by online-judge-template-generator v4.6.0 (https://github.com/online-judge-tools/template-generator) int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); constexpr char endl = '\n'; int N, M; cin >> N >> M; vector L(M), R(M), P(M); REP (i, M) { cin >> L[i] >> R[i] >> P[i]; -- L[i]; } auto ans = solve(N, M, L, R, P); cout << ans << endl; return 0; }