結果
問題 | No.1222 -101 |
ユーザー |
![]() |
提出日時 | 2022-11-02 21:30:38 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 212 ms / 2,000 ms |
コード長 | 28,974 bytes |
コンパイル時間 | 3,406 ms |
コンパイル使用メモリ | 247,900 KB |
最終ジャッジ日時 | 2025-02-08 16:55:04 |
ジャッジサーバーID (参考情報) |
judge5 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 35 |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"#pragma GCC optimize("Ofast")#pragma GCC optimize("unroll-loops")#include <bits/stdc++.h>using namespace std;using ll = long long;using pi = pair<ll, ll>;using vi = vector<ll>;using u32 = unsigned int;using u64 = unsigned long long;using i128 = __int128;template <class T>using vc = vector<T>;template <class T>using vvc = vector<vc<T>>;template <class T>using vvvc = vector<vvc<T>>;template <class T>using vvvvc = vector<vvvc<T>>;template <class T>using vvvvvc = vector<vvvvc<T>>;template <class T>using pq = priority_queue<T>;template <class T>using pqg = priority_queue<T, vector<T>, greater<T>>;#define vec(type, name, ...) vector<type> name(__VA_ARGS__)#define vv(type, name, h, ...) \vector<vector<type>> name(h, vector<type>(__VA_ARGS__))#define vvv(type, name, h, w, ...) \vector<vector<vector<type>>> name( \h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))#define vvvv(type, name, a, b, c, ...) \vector<vector<vector<vector<type>>>> name( \a, vector<vector<vector<type>>>( \b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))// https://trap.jp/post/1224/#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)#define FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c))#define overload4(a, b, c, d, e, ...) e#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)#define FOR_R(...) \overload4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)#define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s))#define all(x) x.begin(), x.end()#define len(x) ll(x.size())#define elif else if#define eb emplace_back#define mp make_pair#define mt make_tuple#define fi first#define se second#define stoi stolltemplate <typename T, typename U>T SUM(const vector<U> &A) {T sum = 0;for (auto &&a: A) sum += a;return sum;}#define MIN(v) *min_element(all(v))#define MAX(v) *max_element(all(v))#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())int popcnt(int x) { return __builtin_popcount(x); }int popcnt(u32 x) { return __builtin_popcount(x); }int popcnt(ll x) { return __builtin_popcountll(x); }int popcnt(u64 x) { return __builtin_popcountll(x); }// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }template <typename T>T pick(deque<T> &que) {T a = que.front();que.pop_front();return a;}template <typename T>T pick(pq<T> &que) {T a = que.top();que.pop();return a;}template <typename T>T pick(pqg<T> &que) {assert(que.size());T a = que.top();que.pop();return a;}template <typename T>T pick(vc<T> &que) {assert(que.size());T a = que.back();que.pop_back();return a;}template <typename T, typename U>T ceil(T x, U y) {return (x > 0 ? (x + y - 1) / y : x / y);}template <typename T, typename U>T floor(T x, U y) {return (x > 0 ? x / y : (x - y + 1) / y);}template <typename T, typename U>pair<T, T> divmod(T x, U y) {T q = floor(x, y);return {q, x - q * y};}template <typename F>ll binary_search(F check, ll ok, ll ng) {assert(check(ok));while (abs(ok - ng) > 1) {auto x = (ng + ok) / 2;tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));}return ok;}template <typename F>double binary_search_real(F check, double ok, double ng, int iter = 100) {FOR(iter) {double x = (ok + ng) / 2;tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));}return (ok + ng) / 2;}template <class T, class S>inline bool chmax(T &a, const S &b) {return (a < b ? a = b, 1 : 0);}template <class T, class S>inline bool chmin(T &a, const S &b) {return (a > b ? a = b, 1 : 0);}vc<int> s_to_vi(const string &S, char first_char) {vc<int> A(S.size());FOR(i, S.size()) { A[i] = S[i] - first_char; }return A;}template <typename T, typename U>vector<T> cumsum(vector<U> &A, int off = 1) {int N = A.size();vector<T> B(N + 1);FOR(i, N) { B[i + 1] = B[i] + A[i]; }if (off == 0) B.erase(B.begin());return B;}template <typename CNT, typename T>vc<CNT> bincount(const vc<T> &A, int size) {vc<CNT> C(size);for (auto &&x: A) { ++C[x]; }return C;}// stabletemplate <typename T>vector<int> argsort(const vector<T> &A) {vector<int> ids(A.size());iota(all(ids), 0);sort(all(ids),[&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });return ids;}// A[I[0]], A[I[1]], ...template <typename T>vc<T> rearrange(const vc<T> &A, const vc<int> &I) {int n = len(I);vc<T> B(n);FOR(i, n) B[i] = A[I[i]];return B;}#line 1 "/home/maspy/compro/library/other/io.hpp"// based on yosupo's fastio#include <unistd.h>namespace detail {template <typename T, decltype(&T::is_modint) = &T::is_modint>std::true_type check_value(int);template <typename T>std::false_type check_value(long);} // namespace detailtemplate <typename T>struct is_modint : decltype(detail::check_value<T>(0)) {};template <typename T>using is_modint_t = enable_if_t<is_modint<T>::value>;template <typename T>using is_not_modint_t = enable_if_t<!is_modint<T>::value>;struct Scanner {FILE *fp;char line[(1 << 15) + 1];size_t st = 0, ed = 0;void reread() {memmove(line, line + st, ed - st);ed -= st;st = 0;ed += fread(line + ed, 1, (1 << 15) - ed, fp);line[ed] = '\0';}bool succ() {while (true) {if (st == ed) {reread();if (st == ed) return false;}while (st != ed && isspace(line[st])) st++;if (st != ed) break;}if (ed - st <= 50) {bool sep = false;for (size_t i = st; i < ed; i++) {if (isspace(line[i])) {sep = true;break;}}if (!sep) reread();}return true;}template <class T, enable_if_t<is_same<T, string>::value, int> = 0>bool read_single(T &ref) {if (!succ()) return false;while (true) {size_t sz = 0;while (st + sz < ed && !isspace(line[st + sz])) sz++;ref.append(line + st, sz);st += sz;if (!sz || st != ed) break;reread();}return true;}template <class T, enable_if_t<is_integral<T>::value, int> = 0>bool read_single(T &ref) {if (!succ()) return false;bool neg = false;if (line[st] == '-') {neg = true;st++;}ref = T(0);while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }if (neg) ref = -ref;return true;}template <class T, is_modint_t<T> * = nullptr>bool read_single(T &ref) {long long val = 0;bool f = read_single(val);ref = T(val);return f;}bool read_single(double &ref) {string s;if (!read_single(s)) return false;ref = std::stod(s);return true;}bool read_single(char &ref) {string s;if (!read_single(s) || s.size() != 1) return false;ref = s[0];return true;}template <class T>bool read_single(vector<T> &ref) {for (auto &d: ref) {if (!read_single(d)) return false;}return true;}template <class T, class U>bool read_single(pair<T, U> &p) {return (read_single(p.first) && read_single(p.second));}template <class A, class B, class C>bool read_single(tuple<A, B, C> &p) {return (read_single(get<0>(p)) && read_single(get<1>(p))&& read_single(get<2>(p)));}template <class A, class B, class C, class D>bool read_single(tuple<A, B, C, D> &p) {return (read_single(get<0>(p)) && read_single(get<1>(p))&& read_single(get<2>(p)) && read_single(get<3>(p)));}void read() {}template <class H, class... T>void read(H &h, T &... t) {bool f = read_single(h);assert(f);read(t...);}Scanner(FILE *fp) : fp(fp) {}};struct Printer {Printer(FILE *_fp) : fp(_fp) {}~Printer() { flush(); }static constexpr size_t SIZE = 1 << 15;FILE *fp;char line[SIZE], small[50];size_t pos = 0;void flush() {fwrite(line, 1, pos, fp);pos = 0;}void write(const char &val) {if (pos == SIZE) flush();line[pos++] = val;}template <class T, enable_if_t<is_integral<T>::value, int> = 0>void write(T val) {if (pos > (1 << 15) - 50) flush();if (val == 0) {write('0');return;}if (val < 0) {write('-');val = -val; // todo min}size_t len = 0;while (val) {small[len++] = char(0x30 | (val % 10));val /= 10;}for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }pos += len;}void write(const string &s) {for (char c: s) write(c);}void write(const char *s) {size_t len = strlen(s);for (size_t i = 0; i < len; i++) write(s[i]);}void write(const double &x) {ostringstream oss;oss << fixed << setprecision(15) << x;string s = oss.str();write(s);}void write(const long double &x) {ostringstream oss;oss << fixed << setprecision(15) << x;string s = oss.str();write(s);}template <class T, is_modint_t<T> * = nullptr>void write(T &ref) {write(ref.val);}template <class T>void write(const vector<T> &val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) write(' ');write(val[i]);}}template <class T, class U>void write(const pair<T, U> &val) {write(val.first);write(' ');write(val.second);}template <class A, class B, class C>void write(const tuple<A, B, C> &val) {auto &[a, b, c] = val;write(a), write(' '), write(b), write(' '), write(c);}template <class A, class B, class C, class D>void write(const tuple<A, B, C, D> &val) {auto &[a, b, c, d] = val;write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d);}template <class A, class B, class C, class D, class E>void write(const tuple<A, B, C, D, E> &val) {auto &[a, b, c, d, e] = val;write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e);}template <class A, class B, class C, class D, class E, class F>void write(const tuple<A, B, C, D, E, F> &val) {auto &[a, b, c, d, e, f] = val;write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f);}template <class T, size_t S>void write(const array<T, S> &val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) write(' ');write(val[i]);}}void write(i128 val) {string s;bool negative = 0;if(val < 0){negative = 1;val = -val;}while (val) {s += '0' + int(val % 10);val /= 10;}if(negative) s += "-";reverse(all(s));if (len(s) == 0) s = "0";write(s);}};Scanner scanner = Scanner(stdin);Printer printer = Printer(stdout);void flush() { printer.flush(); }void print() { printer.write('\n'); }template <class Head, class... Tail>void print(Head &&head, Tail &&... tail) {printer.write(head);if (sizeof...(Tail)) printer.write(' ');print(forward<Tail>(tail)...);}void read() {}template <class Head, class... Tail>void read(Head &head, Tail &... tail) {scanner.read(head);read(tail...);}#define INT(...) \int __VA_ARGS__; \read(__VA_ARGS__)#define LL(...) \ll __VA_ARGS__; \read(__VA_ARGS__)#define STR(...) \string __VA_ARGS__; \read(__VA_ARGS__)#define CHAR(...) \char __VA_ARGS__; \read(__VA_ARGS__)#define DBL(...) \double __VA_ARGS__; \read(__VA_ARGS__)#define VEC(type, name, size) \vector<type> name(size); \read(name)#define VV(type, name, h, w) \vector<vector<type>> name(h, vector<type>(w)); \read(name)void YES(bool t = 1) { print(t ? "YES" : "NO"); }void NO(bool t = 1) { YES(!t); }void Yes(bool t = 1) { print(t ? "Yes" : "No"); }void No(bool t = 1) { Yes(!t); }void yes(bool t = 1) { print(t ? "yes" : "no"); }void no(bool t = 1) { yes(!t); }#line 2 "/home/maspy/compro/library/mod/modint.hpp"template <int mod>struct modint {static constexpr bool is_modint = true;int val;constexpr modint(const ll val = 0) noexcept: val(val >= 0 ? val % mod : (mod - (-val) % mod) % mod) {}bool operator<(const modint &other) const {return val < other.val;} // To use std::mapmodint &operator+=(const modint &p) {if ((val += p.val) >= mod) val -= mod;return *this;}modint &operator-=(const modint &p) {if ((val += mod - p.val) >= mod) val -= mod;return *this;}modint &operator*=(const modint &p) {val = (int)(1LL * val * p.val % mod);return *this;}modint &operator/=(const modint &p) {*this *= p.inverse();return *this;}modint operator-() const { return modint(-val); }modint operator+(const modint &p) const { return modint(*this) += p; }modint operator-(const modint &p) const { return modint(*this) -= p; }modint operator*(const modint &p) const { return modint(*this) *= p; }modint operator/(const modint &p) const { return modint(*this) /= p; }bool operator==(const modint &p) const { return val == p.val; }bool operator!=(const modint &p) const { return val != p.val; }modint inverse() const {int a = val, b = mod, u = 1, v = 0, t;while (b > 0) {t = a / b;swap(a -= t * b, b), swap(u -= t * v, v);}return modint(u);}modint pow(int64_t n) const {modint ret(1), mul(val);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}static constexpr int get_mod() { return mod; }};struct ArbitraryModInt {static constexpr bool is_modint = true;int val;ArbitraryModInt() : val(0) {}ArbitraryModInt(int64_t y): val(y >= 0 ? y % get_mod(): (get_mod() - (-y) % get_mod()) % get_mod()) {}bool operator<(const ArbitraryModInt &other) const {return val < other.val;} // To use std::map<ArbitraryModInt, T>static int &get_mod() {static int mod = 0;return mod;}static void set_mod(int md) { get_mod() = md; }ArbitraryModInt &operator+=(const ArbitraryModInt &p) {if ((val += p.val) >= get_mod()) val -= get_mod();return *this;}ArbitraryModInt &operator-=(const ArbitraryModInt &p) {if ((val += get_mod() - p.val) >= get_mod()) val -= get_mod();return *this;}ArbitraryModInt &operator*=(const ArbitraryModInt &p) {long long a = (long long)val * p.val;int xh = (int)(a >> 32), xl = (int)a, d, m;asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(get_mod()));val = m;return *this;}ArbitraryModInt &operator/=(const ArbitraryModInt &p) {*this *= p.inverse();return *this;}ArbitraryModInt operator-() const { return ArbitraryModInt(get_mod() - val); }ArbitraryModInt operator+(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) += p;}ArbitraryModInt operator-(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) -= p;}ArbitraryModInt operator*(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) *= p;}ArbitraryModInt operator/(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) /= p;}bool operator==(const ArbitraryModInt &p) const { return val == p.val; }bool operator!=(const ArbitraryModInt &p) const { return val != p.val; }ArbitraryModInt inverse() const {int a = val, b = get_mod(), u = 1, v = 0, t;while (b > 0) {t = a / b;swap(a -= t * b, b), swap(u -= t * v, v);}return ArbitraryModInt(u);}ArbitraryModInt pow(int64_t n) const {ArbitraryModInt ret(1), mul(val);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}};template <typename mint>mint inv(int n) {static const int mod = mint::get_mod();static vector<mint> dat = {0, 1};assert(0 <= n);if (n >= mod) n %= mod;while (int(dat.size()) <= n) {int k = dat.size();auto q = (mod + k - 1) / k;int r = k * q - mod;dat.emplace_back(dat[r] * mint(q));}return dat[n];}template <typename mint>mint fact(int n) {static const int mod = mint::get_mod();static vector<mint> dat = {1, 1};assert(0 <= n);if (n >= mod) return 0;while (int(dat.size()) <= n) {int k = dat.size();dat.emplace_back(dat[k - 1] * mint(k));}return dat[n];}template <typename mint>mint fact_inv(int n) {static const int mod = mint::get_mod();static vector<mint> dat = {1, 1};assert(0 <= n && n < mod);while (int(dat.size()) <= n) {int k = dat.size();dat.emplace_back(dat[k - 1] * inv<mint>(k));}return dat[n];}template <class mint, class... Ts>mint fact_invs(Ts... xs) {return (mint(1) * ... * fact_inv<mint>(xs));}template <typename mint, class Head, class... Tail>mint multinomial(Head &&head, Tail &&... tail) {return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);}template <typename mint>mint C_dense(int n, int k) {static vvc<mint> C;static int H = 0, W = 0;auto calc = [&](int i, int j) -> mint {if (i == 0) return (j == 0 ? mint(1) : mint(0));return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);};if (W <= k) {FOR(i, H) {C[i].resize(k + 1);FOR(j, W, k + 1) { C[i][j] = calc(i, j); }}W = k + 1;}if (H <= n) {C.resize(n + 1);FOR(i, H, n + 1) {C[i].resize(W);FOR(j, W) { C[i][j] = calc(i, j); }}H = n + 1;}return C[n][k];}template <typename mint, bool large = false, bool dense = false>mint C(ll n, ll k) {assert(n >= 0);if (k < 0 || n < k) return 0;if (dense) return C_dense<mint>(n, k);if (!large) return fact<mint>(n) * fact_inv<mint>(k) * fact_inv<mint>(n - k);k = min(k, n - k);mint x(1);FOR(i, k) { x *= mint(n - i); }x *= fact_inv<mint>(k);return x;}template <typename mint, bool large = false>mint C_inv(ll n, ll k) {assert(n >= 0);assert(0 <= k && k <= n);if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);return mint(1) / C<mint, 1>(n, k);}// [x^d] (1-x) ^ {-n} の計算template <typename mint, bool large = false, bool dense = false>mint C_negative(ll n, ll d) {assert(n >= 0);if (d < 0) return mint(0);if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }return C<mint, large, dense>(n + d - 1, d);}using modint107 = modint<1000000007>;using modint998 = modint<998244353>;using amint = ArbitraryModInt;#line 2 "/home/maspy/compro/library/alg/group/add.hpp"template <typename E>struct Group_Add {using X = E;using value_type = X;static constexpr X op(const X &x, const X &y) noexcept { return x + y; }static constexpr X inverse(const X &x) noexcept { return -x; }static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }static constexpr X unit() { return X(0); }static constexpr bool commute = true;};#line 3 "/home/maspy/compro/library/ds/fenwick.hpp"template <typename AbelGroup>struct FenwickTree {using E = typename AbelGroup::value_type;int n;vector<E> dat;E total;FenwickTree(int n = 0) : n(n) {assert(AbelGroup::commute);reset(n);}FenwickTree(const vector<E>& v) {assert(AbelGroup::commute);build(v);}void build(const vc<E>& v) {n = len(v);total = AbelGroup::unit();for (int i = 0; i < n; ++i) total = AbelGroup::op(total, v[i]);dat = v;for (int i = 1; i <= n; ++i) {int j = i + (i & -i);if (j <= n) dat[j - 1] = AbelGroup::op(dat[i - 1], dat[j - 1]);}}void reset(int sz = 0) {if (sz) n = sz;total = AbelGroup::unit();dat.assign(n, AbelGroup::unit());}E prod(int k) {E ret = AbelGroup::unit();for (; k > 0; k -= k & -k) ret = AbelGroup::op(ret, dat[k - 1]);return ret;}E prod(int L, int R) {E pos = AbelGroup::unit();while (L < R) {pos = AbelGroup::op(pos, dat[R - 1]);R -= R & -R;}E neg = AbelGroup::unit();while (R < L) {neg = AbelGroup::op(neg, dat[L - 1]);L -= L & -L;}return AbelGroup::op(pos, AbelGroup::inverse(neg));}E prod_all() { return total; }E sum(int k) { return prod(k); }E sum(int L, int R) { return prod(L, R); }E sum_all() { return total; }void multiply(int k, E x) {total = AbelGroup::op(total, x);for (++k; k <= n; k += k & -k) dat[k - 1] = AbelGroup::op(dat[k - 1], x);}void add(int k, E x) { multiply(k, x); }template <class F>int max_right(F& check) {assert(check(E(0)));ll i = 0;E s = AbelGroup::unit();int k = 1;int N = dat.size() + 1;while (2 * k < N) k *= 2;while (k) {if (i + k < N && check(AbelGroup::op(s, dat[i + k - 1]))) {i += k;s = AbelGroup::op(s, dat[i - 1]);}k >>= 1;}return i;}int find_kth(E k) {auto check = [&](E x) -> bool { return x <= k; };return max_right(check);}void debug() { print("fenwick", dat); }};#line 2 "/home/maspy/compro/library/ds/lazysegtree.hpp"template <typename Lazy>struct LazySegTree {using Monoid_X = typename Lazy::X_structure;using Monoid_A = typename Lazy::A_structure;using X = typename Monoid_X::value_type;using A = typename Monoid_A::value_type;int n, log, size;vc<X> dat;vc<A> laz;LazySegTree() : LazySegTree(0) {}LazySegTree(int n) : LazySegTree(vc<X>(n, Monoid_X::unit())) {}LazySegTree(vc<X> v) : n(len(v)) {log = 1;while ((1 << log) < n) ++log;size = 1 << log;dat.assign(size << 1, Monoid_X::unit());laz.assign(size, Monoid_A::unit());FOR(i, n) dat[size + i] = v[i];FOR3_R(i, 1, size) update(i);}template <typename F>LazySegTree(int n, F f) : n(n) {log = 1;while ((1 << log) < n) ++log;size = 1 << log;dat.assign(size << 1, Monoid_X::unit());laz.assign(size, Monoid_A::unit());FOR(i, n) dat[size + i] = f(i);FOR3_R(i, 1, size) update(i);}void reset() {fill(all(dat), Monoid_X::unit());fill(all(laz), Monoid_A::unit());}void reset(const vc<X>& v) {assert(len(v) == n);reset();FOR(i, n) dat[size + i] = v[i];FOR3_R(i, 1, size) update(i);}void update(int k) { dat[k] = Monoid_X::op(dat[2 * k], dat[2 * k + 1]); }void all_apply(int k, A a) {dat[k] = Lazy::act(dat[k], a);if (k < size) laz[k] = Monoid_A::op(laz[k], a);}void push(int k) {all_apply(2 * k, laz[k]);all_apply(2 * k + 1, laz[k]);laz[k] = Monoid_A::unit();}void set(int p, X x) {assert(0 <= p && p < n);p += size;for (int i = log; i >= 1; i--) push(p >> i);dat[p] = x;for (int i = 1; i <= log; i++) update(p >> i);}X get(int p) {assert(0 <= p && p < n);p += size;for (int i = log; i >= 1; i--) push(p >> i);return dat[p];}vc<X> get_all() {FOR(i, size) push(i);return {dat.begin() + size, dat.begin() + size + n};}X prod(int l, int r) {assert(0 <= l && l <= r && r <= n);if (l == r) return Monoid_X::unit();l += size;r += size;for (int i = log; i >= 1; i--) {if (((l >> i) << i) != l) push(l >> i);if (((r >> i) << i) != r) push((r - 1) >> i);}X xl = Monoid_X::unit(), xr = Monoid_X::unit();while (l < r) {if (l & 1) xl = Monoid_X::op(xl, dat[l++]);if (r & 1) xr = Monoid_X::op(dat[--r], xr);l >>= 1;r >>= 1;}return Monoid_X::op(xl, xr);}X prod_all() { return dat[1]; }void apply(int p, A a) {assert(0 <= p && p < n);p += size;dat[p] = Lazy::act(dat[p], a);for (int i = 1; i <= log; i++) update(p >> i);}void apply(int l, int r, A a) {assert(0 <= l && l <= r && r <= n);if (l == r) return;l += size;r += size;for (int i = log; i >= 1; i--) {if (((l >> i) << i) != l) push(l >> i);if (((r >> i) << i) != r) push((r - 1) >> i);}{int l2 = l, r2 = r;while (l < r) {if (l & 1) all_apply(l++, a);if (r & 1) all_apply(--r, a);l >>= 1;r >>= 1;}l = l2;r = r2;}for (int i = 1; i <= log; i++) {if (((l >> i) << i) != l) update(l >> i);if (((r >> i) << i) != r) update((r - 1) >> i);}}template <typename C>int max_right(C& check, int l) {assert(0 <= l && l <= n);assert(check(Monoid_X::unit()));if (l == n) return n;l += size;for (int i = log; i >= 1; i--) push(l >> i);X sm = Monoid_X::unit();do {while (l % 2 == 0) l >>= 1;if (!check(Monoid_X::op(sm, dat[l]))) {while (l < size) {push(l);l = (2 * l);if (check(Monoid_X::op(sm, dat[l]))) {sm = Monoid_X::op(sm, dat[l]);l++;}}return l - size;}sm = Monoid_X::op(sm, dat[l]);l++;} while ((l & -l) != l);return n;}template <typename C>int min_left(C& check, int r) {assert(0 <= r && r <= n);assert(check(Monoid_X::unit()));if (r == 0) return 0;r += size;for (int i = log; i >= 1; i--) push((r - 1) >> i);X sm = Monoid_X::unit();do {r--;while (r > 1 && (r % 2)) r >>= 1;if (!check(Monoid_X::op(dat[r], sm))) {while (r < size) {push(r);r = (2 * r + 1);if (check(Monoid_X::op(dat[r], sm))) {sm = Monoid_X::op(dat[r], sm);r--;}}return r + 1 - size;}sm = Monoid_X::op(dat[r], sm);} while ((r & -r) != r);return 0;}void debug() { print("lazysegtree getall:", get_all()); }};#line 2 "/home/maspy/compro/library/alg/group/mul.hpp"template <class T>struct Group_Mul {using value_type = T;using X = T;static constexpr X op(const X &x, const X &y) noexcept { return x * y; }static constexpr X inverse(const X &x) noexcept { return X(1) / x; }static constexpr X unit() { return X(1); }static constexpr bool commute = true;};#line 3 "/home/maspy/compro/library/alg/lazy/add_mul.hpp"template <typename E>struct Lazy_Add_Mul {using MX = Group_Add<E>;using MA = Group_Mul<E>;using X_structure = MX;using A_structure = MA;using X = typename MX::value_type;using A = typename MA::value_type;static constexpr X act(const X &x, const A &a) { return x * a; }};#line 7 "main.cpp"using mint = modint107;void solve() {LL(N, M);// サイクルなしなので、整合的な符号は存在// 1 であることが保証されているか?vc<pi> LR; // zerovi A(N + 1);ll cons_1 = 0;FOR(M) {LL(L, R, p);--L;if (p != 0) {++cons_1;A[L]++, A[R]--;}if (p == 0) { LR.eb(L, R); }}A = cumsum<ll>(A, 0);ll one = 0;for (auto&& x: A)if (x > 0) ++one;mint cf = mint(2).pow(one - cons_1);// いま 0 のところに 012 を割り当てる。LR 条件のみ気にしてvc<int> R_to_L(N + 1, -1);for (auto&& [L, R]: LR) { R_to_L[R] = L; }using Lazy = Lazy_Add_Mul<mint>;LazySegTree<Lazy> seg(vc<mint>(N + 1, 0));seg.set(0, mint(1));FOR(i, N) {if (A[i] == 0) {// dp[i + 1] = SUM<mint>(dp);// FOR(k, i + 1) dp[k] += dp[k];seg.set(i + 1, seg.prod_all());seg.apply(0, i + 1, mint(2));}int L = R_to_L[i + 1];// FOR(j, L + 1) dp[j] = mint(0);seg.apply(0, L + 1, mint(0));}mint ANS = cf * seg.prod_all();print(ANS);}signed main() {cout << fixed << setprecision(15);ll T = 1;// LL(T);FOR(T) solve();return 0;}