結果
| 問題 | No.1222 -101 |
| ユーザー |
 noimi
|
| 提出日時 | 2020-09-04 22:54:06 |
| 言語 | C++17 (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 147 ms / 2,000 ms |
| コード長 | 25,871 bytes |
| コンパイル時間 | 5,434 ms |
| コンパイル使用メモリ | 277,348 KB |
| 実行使用メモリ | 24,628 KB |
| 最終ジャッジ日時 | 2023-08-17 20:32:47 |
| 合計ジャッジ時間 | 9,393 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge13 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
4,380 KB |
| testcase_01 | AC | 1 ms
4,376 KB |
| testcase_02 | AC | 2 ms
4,376 KB |
| testcase_03 | AC | 2 ms
4,380 KB |
| testcase_04 | AC | 1 ms
4,376 KB |
| testcase_05 | AC | 2 ms
4,380 KB |
| testcase_06 | AC | 2 ms
4,380 KB |
| testcase_07 | AC | 2 ms
4,380 KB |
| testcase_08 | AC | 2 ms
4,376 KB |
| testcase_09 | AC | 2 ms
4,380 KB |
| testcase_10 | AC | 36 ms
16,676 KB |
| testcase_11 | AC | 37 ms
16,624 KB |
| testcase_12 | AC | 136 ms
24,380 KB |
| testcase_13 | AC | 135 ms
24,628 KB |
| testcase_14 | AC | 136 ms
24,488 KB |
| testcase_15 | AC | 89 ms
20,724 KB |
| testcase_16 | AC | 111 ms
22,592 KB |
| testcase_17 | AC | 128 ms
24,104 KB |
| testcase_18 | AC | 87 ms
20,744 KB |
| testcase_19 | AC | 101 ms
21,708 KB |
| testcase_20 | AC | 113 ms
22,944 KB |
| testcase_21 | AC | 112 ms
22,804 KB |
| testcase_22 | AC | 2 ms
4,380 KB |
| testcase_23 | AC | 1 ms
4,380 KB |
| testcase_24 | AC | 1 ms
4,376 KB |
| testcase_25 | AC | 1 ms
4,380 KB |
| testcase_26 | AC | 2 ms
4,376 KB |
| testcase_27 | AC | 1 ms
4,380 KB |
| testcase_28 | AC | 2 ms
4,376 KB |
| testcase_29 | AC | 2 ms
4,380 KB |
| testcase_30 | AC | 2 ms
4,380 KB |
| testcase_31 | AC | 1 ms
4,376 KB |
| testcase_32 | AC | 147 ms
24,376 KB |
| testcase_33 | AC | 144 ms
24,344 KB |
| testcase_34 | AC | 110 ms
24,284 KB |
| testcase_35 | AC | 108 ms
24,340 KB |
| testcase_36 | AC | 114 ms
24,424 KB |
| testcase_37 | AC | 117 ms
24,420 KB |
| testcase_38 | AC | 110 ms
24,624 KB |
コンパイルメッセージ
main.cpp:735:1: 警告: ISO C++ では型の無い ‘main’ の宣言を禁止しています [-Wreturn-type]
735 | main() {
| ^~~~
ソースコード
#pragma region Macros
#pragma GCC optimize("O3")
#pragma GCC target("avx2,avx")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
#define ll long long
#define ld long double
#define rep2(i, a, b) for(ll i = a; i <= b; ++i)
#define rep(i, n) for(ll i = 0; i < n; ++i)
#define rep3(i, a, b) for(ll i = a; i >= b; --i)
#define pii pair<int, int>
#define pll pair<ll, ll>
#define pb push_back
#define eb emplace_back
#define vi vector<int>
#define vll vector<ll>
#define vpi vector<pii>
#define vpll vector<pll>
#define overload2(_1, _2, name, ...) name
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
IN(name)
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
IN(name)
#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__))))
#define fi first
#define se second
#define all(c) begin(c), end(c)
#define ios ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
using namespace std;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
#define si(c) (int)(c).size()
#define INT(...) \
int __VA_ARGS__; \
IN(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
IN(__VA_ARGS__)
#define ULL(...) \
ull __VA_ARGS__; \
IN(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
IN(__VA_ARGS__)
#define CHR(...) \
char __VA_ARGS__; \
IN(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
IN(__VA_ARGS__)
#define LD(...) \
ld __VA_ARGS__; \
IN(__VA_ARGS__)
int scan() { return getchar(); }
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(long double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T> void scan(vector<T> &);
template <class T> void scan(vector<T> &a) {
for(auto &i : a) scan(i);
}
template <class T> void scan(T &a) { cin >> a; }
void IN() {}
template <class Head, class... Tail> void IN(Head &head, Tail &... tail) {
scan(head);
IN(tail...);
}
string stin() {
string s;
cin >> s;
return s;
}
template <class T, class S> inline bool chmax(T &a, S b) {
if(a < b) {
a = b;
return 1;
}
return 0;
}
template <class T, class S> inline bool chmin(T &a, S b) {
if(a > b) {
a = b;
return 1;
}
return 0;
}
vi iota(int n) {
vi a(n);
iota(all(a), 0);
return a;
}
template <class T> void UNIQUE(vector<T> &x) {
sort(all(x));
x.erase(unique(all(x)), x.end());
}
int in() {
int x;
cin >> x;
return x;
}
ll lin() {
unsigned long long x;
cin >> x;
return x;
}
void print() { putchar(' '); }
void print(bool a) { cout << a; }
void print(int a) { cout << a; }
void print(long long a) { cout << a; }
void print(char a) { cout << a; }
void print(string &a) { cout << a; }
void print(double a) { cout << a; }
template <class T> void print(const vector<T> &);
template <class T, size_t size> void print(const array<T, size> &);
template <class T, class L> void print(const pair<T, L> &p);
template <class T, size_t size> void print(const T (&)[size]);
template <class T> void print(const vector<T> &a) {
if(a.empty()) return;
print(a[0]);
for(auto i = a.begin(); ++i != a.end();) {
cout << " ";
print(*i);
}
cout << endl;
}
template <class T> void print(const deque<T> &a) {
if(a.empty()) return;
print(a[0]);
for(auto i = a.begin(); ++i != a.end();) {
cout << " ";
print(*i);
}
}
template <class T, size_t size> void print(const array<T, size> &a) {
print(a[0]);
for(auto i = a.begin(); ++i != a.end();) {
cout << " ";
print(*i);
}
}
template <class T, class L> void print(const pair<T, L> &p) {
cout << '(';
print(p.first);
cout << ",";
print(p.second);
cout << ')';
}
template <class T> void print(set<T> &x) {
for(auto e : x) print(e), cout << " ";
cout << endl;
}
template <class T> void print(multiset<T> &x) {
for(auto e : x) print(e), cout << " ";
cout << endl;
}
template <class T, size_t size> void print(const T (&a)[size]) {
print(a[0]);
for(auto i = a; ++i != end(a);) {
cout << " ";
print(*i);
}
}
template <class T> void print(const T &a) { cout << a; }
int out() {
putchar('\n');
return 0;
}
template <class T> int out(const T &t) {
print(t);
putchar('\n');
return 0;
}
template <class Head, class... Tail> int out(const Head &head, const Tail &... tail) {
print(head);
putchar(' ');
out(tail...);
return 0;
}
ll gcd(ll a, ll b) {
while(b) {
ll c = b;
b = a % b;
a = c;
}
return a;
}
ll lcm(ll a, ll b) {
if(!a || !b) return 0;
return a * b / gcd(a, b);
}
vector<pll> factor(ll x) {
vector<pll> ans;
for(ll i = 2; i * i <= x; i++)
if(x % i == 0) {
ans.push_back({i, 1});
while((x /= i) % i == 0) ans.back().second++;
}
if(x != 1) ans.push_back({x, 1});
return ans;
}
template <class T> vector<T> divisor(T x) {
vector<T> ans;
for(T i = 1; i * i <= x; i++)
if(x % i == 0) {
ans.pb(i);
if(i * i != x) ans.pb(x / i);
}
return ans;
}
template <typename T> void zip(vector<T> &x) {
vector<T> y = x;
sort(all(y));
for(int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); }
}
int popcount(ll x) { return __builtin_popcountll(x); }
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int n) { return uniform_int_distribution<int>(0, n - 1)(rng); }
ll rndll(ll n) { return uniform_int_distribution<ll>(0, n - 1)(rng); }
template <typename T> void shuffle(vector<T> &v) {
rep3(i, v.size() - 1, 1) { swap(v[i], v[rnd(i)]); }
}
#define endl '\n'
vector<string> YES{"NO", "YES"};
vector<string> Yes{"No", "Yes"};
vector<string> yes{"no", "yes"};
#ifdef _LOCAL
#undef endl
#define debug(x) \
cout << #x << ": "; \
print(x); \
cout << endl;
void err() {}
template <class T> void err(const T &t) {
print(t);
cout << " ";
}
template <class Head, class... Tail> void err(const Head &head, const Tail &... tail) {
print(head);
putchar(' ');
out(tail...);
}
#else
#define debug(x)
template <class... T> void err(const T &...) {}
#endif
template <typename T> struct edge {
int from, to;
T cost;
int id;
edge(int to, T cost) : from(-1), to(to), cost(cost) {}
edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
edge(int from, int to, T cost, int id) : from(from), to(to), cost(cost), id(id) {}
edge &operator=(const int &x) {
to = x;
return *this;
}
operator int() const { return to; }
};
template <typename T> using Edges = vector<edge<T>>;
struct Graph : vector<vector<int>> {
using vector<vector<int>>::vector;
Graph(int n, int m) : vector(n) { read(m); }
inline void add(int a, int b, bool directed = false) {
(*this)[a].emplace_back(b);
if(!directed) (*this)[b].emplace_back(a);
}
void read(int n = -1, int offset = 1, bool directed = false) {
if(n == -1) n = this->size() - 1;
int a, b;
while(n--) {
cin >> a >> b;
Graph::add(a - offset, b - offset, directed);
}
}
};
template <typename T> struct WeightedGraph : vector<Edges<T>> {
using vector<Edges<T>>::vector;
inline void add(int a, int b, T c, bool directed = false) {
(*this)[a].emplace_back(b, c);
if(!directed) (*this)[b].emplace_back(a, c);
}
void read(int n = -1, int offset = 1) {
if(n == -1) n = this->size() - 1;
int a, b;
T c;
while(n--) {
cin >> a >> b >> c;
WeightedGraph::add(a - offset, b - offset, c);
}
}
};
struct Setup_io {
Setup_io() {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
cout << fixed << setprecision(15);
}
} setup_io;
#define i128 __int128_t
#define ull unsigned long long int
#define TEST \
INT(testcases); \
while(testcases--)
#pragma endregion
template <typename T> static constexpr T inf = numeric_limits<T>::max() / 2;
// _________コーディングはここから！！___________
template <typename T = long long> struct SegmentTree {
using F = function<T(T, T)>;
#define clz(x) __builtin_clz(x)
SegmentTree(int n, const F f, const T &unit) : f(f), unit(unit), sz(n - 1 ? 1 << (32 - clz(n - 1)) : 1) { seg.assign(2 * sz, unit); }
SegmentTree(vector<T> &a, const F f, const T &unit) : f(f), sz((int)a.size() > 1 ? 1 << (32 - clz(a.size() - 1)) : 1), unit(unit) {
int n0 = a.size();
seg.assign(2 * sz, unit);
for(int i = 0; i < n0; ++i) seg[i + sz] = a[i];
for(int i = sz - 1; i > 0; --i) seg[i] = f(seg[i << 1], seg[(i << 1) | 1]);
}
const int sz;
vector<T> seg;
const F f;
const T unit;
void set(int k, T x) { seg[k + sz] = x; }
void build() {
for(int i = sz - 1; i > 0; --i) seg[i] = f(seg[i << 1], seg[(i << 1) | 1]);
}
T query(int l, int r) {
T x = unit;
for(int d = r - l; d >= 1; d = r - l) {
int L = l | ((1U << 31) >> clz(d));
int k = __builtin_ctz(L);
x = f(x, seg[(sz | l) >> k]);
l += L & (-L);
}
return x;
}
void update(int i, T x) {
int k = i + sz;
seg[k] = x;
for(k = k >> 1; k > 0; k >>= 1) { seg[k] = f(seg[k << 1], seg[(k << 1) | 1]); }
}
void add(int i, T x) {
int k = i + sz;
seg[k] += x;
for(k = k >> 1; k > 0; k >>= 1) { seg[k] = f(seg[k << 1], seg[(k << 1) | 1]); }
}
SegmentTree() = default;
T operator[](int k) const { return seg[sz + k]; }
};
template <typename T> struct RMQ : SegmentTree<T> {
RMQ(int n)
: SegmentTree<T>(
n, [](T i, T j) { return max(i, j); }, numeric_limits<T>::min()) {}
RMQ(vector<T> &a)
: SegmentTree<T>(
a, [](T i, T j) { return max(i, j); }, numeric_limits<T>::min()) {}
};
template <typename T> struct RmQ : SegmentTree<T> {
RmQ(int n)
: SegmentTree<T>(
n, [](T i, T j) { return min(i, j); }, numeric_limits<T>::max()) {}
RmQ(vector<T> &a)
: SegmentTree<T>(
a, [](T i, T j) { return min(i, j); }, numeric_limits<T>::max()) {}
};
namespace modular {
constexpr ll MOD = 1000000007;
const int MAXN = 1100000;
template <ll Modulus> class modint {
using u64 = ll;
public:
u64 a;
constexpr modint(const u64 x = 0) noexcept : a(((x % Modulus) + Modulus) % Modulus) {}
constexpr u64 &value() noexcept { return a; }
constexpr const u64 &value() const noexcept { return a; }
constexpr modint operator-() const noexcept { return modint() - *this; }
constexpr modint operator+(const modint rhs) const noexcept { return modint(*this) += rhs; }
constexpr modint operator-(const modint rhs) const noexcept { return modint(*this) -= rhs; }
constexpr modint operator*(const modint rhs) const noexcept { return modint(*this) *= rhs; }
template <typename T> constexpr modint operator^(T rhs) const noexcept { return modint(*this) ^= rhs; }
constexpr modint &operator+=(const modint rhs) noexcept {
a += rhs.a;
if(a >= Modulus) { a -= Modulus; }
return *this;
}
constexpr modint &operator-=(const modint rhs) noexcept {
if(a < rhs.a) { a += Modulus; }
a -= rhs.a;
return *this;
}
constexpr modint &operator*=(const modint rhs) noexcept {
a = a * rhs.a % Modulus;
return *this;
}
constexpr bool operator==(const modint rhs) const noexcept { return a == rhs.a; }
template <typename T> constexpr modint &operator^=(T n) noexcept {
modint<Modulus> res = 1;
modint<Modulus> x = a;
while(n) {
if(n & 1) res *= x;
x *= x;
n >>= 1;
}
a = res.a;
return *this;
}
};
#define mint modint<MOD>
#define vmint vector<mint>
vmint Inv{0, 1}, Prd{1, 1}, Invprd{1, 1};
mint inv(int n) {
if(Inv.size() > n)
return Inv[n];
else {
for(int i = Inv.size(); i <= n; ++i) Inv.emplace_back(Inv[MOD % i] * (-MOD / i));
return Inv[n];
}
}
mint prd(int n) {
if(Prd.size() > n)
return Prd[n];
else
for(int i = Prd.size(); i <= n; ++i) Prd.emplace_back(Prd[i - 1] * i);
return Prd[n];
}
mint invprd(int n) {
if(Invprd.size() > n)
return Invprd[n];
else
for(int i = Invprd.size(); i <= n; ++i) Invprd.emplace_back(Invprd[i - 1] * inv(i));
return Invprd[n];
}
mint modpow(ll a, ll n) {
mint x = a;
return x ^= n;
}
template <ll T> modint<T> operator/(modint<T> l, modint<T> r) {
if(r.a < MAXN) return l * inv(r.a);
return l * (r ^ (MOD - 2));
}
template <typename T, ll S> modint<S> operator/(T l, modint<S> r) { return modint<S>(l) / r; }
template <ll T> modint<T> operator/=(modint<T> &l, modint<T> r) { return l = l / r; }
mint C(int a, int b) {
if(a < 0 || b < 0) return 0;
if(a < b) return 0;
return prd(a) * invprd(b) * invprd(a - b);
}
mint P(int a, int b) {
if(a < 0 || b < 0) return 0;
if(a < b) return 0;
return prd(a) * invprd(a - b);
}
ostream &operator<<(ostream &os, mint a) {
os << a.a;
return os;
}
istream &operator>>(istream &is, mint &a) {
ll x;
is >> x;
a = x;
return is;
}
struct modinfo {
int mod, root;
};
constexpr modinfo base0{1045430273, 3};
constexpr modinfo base1{1051721729, 6};
constexpr modinfo base2{1053818881, 7};
using mint0 = modint<base0.mod>;
using mint1 = modint<base1.mod>;
using mint2 = modint<base2.mod>;
template <int mod> void FMT(vector<modint<mod>> &f, bool inv = false) {
using V = vector<modint<mod>>;
static V g(30), ig(30);
if(g.front().a == 0) {
modint<mod> root = 2;
while((root ^ ((mod - 1) / 2)).a == 1) root += 1;
rep(i, 30) g[i] = -(root ^ ((mod - 1) >> (i + 2))), ig[i] = g[i] ^ (mod - 2);
}
int n = size(f);
if(!inv) {
for(int m = n; m >>= 1;) {
modint<mod> w = 1;
for(int s = 0, k = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; ++i, ++j) {
auto x = f[i], y = f[j] * w;
if(x.a >= mod) x.a -= mod;
f[i].a = x.a + y.a, f[j].a = x.a + (mod - y.a);
}
w *= g[__builtin_ctz(++k)];
}
}
} else {
for(int m = 1; m < n; m *= 2) {
modint<mod> w = 1;
for(int s = 0, k = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; ++i, ++j) {
auto x = f[i], y = f[j];
f[i] = x + y, f[j].a = x.a + (mod - y.a), f[j] *= w;
}
w *= ig[__builtin_ctz(++k)];
}
}
}
modint<mod> c;
if(inv)
c = modint<mod>(n) ^ (mod - 2);
else
c = 1;
for(auto &&e : f) e *= c;
}
using Poly = vmint;
Poly operator-(Poly f) {
for(auto &&e : f) e = -e;
return f;
}
Poly &operator+=(Poly &l, const Poly &r) {
l.resize(max(l.size(), r.size()));
rep(i, r.size()) l[i] += r[i];
return l;
}
Poly operator+(Poly l, const Poly &r) { return l += r; }
Poly &operator-=(Poly &l, const Poly &r) {
l.resize(max(l.size(), r.size()));
rep(i, r.size()) l[i] -= r[i];
return l;
}
Poly operator-(Poly l, const Poly &r) { return l -= r; }
Poly &operator<<=(Poly &f, size_t n) { return f.insert(f.begin(), n, 0), f; }
Poly operator<<(Poly f, size_t n) { return f <<= n; }
Poly &operator>>=(Poly &f, size_t n) { return f.erase(f.begin(), f.begin() + min(f.size(), n)), f; }
Poly operator>>(Poly f, size_t n) { return f >>= n; }
constexpr int mod0 = 998244353, mod1 = 1300234241, mod2 = 1484783617;
using M0 = modint<mod0>;
using M1 = modint<mod1>;
using M2 = modint<mod2>;
template <int mod> void mul(vector<modint<mod>> &l, vector<modint<mod>> &r) {
int n = size(l), m = size(r), sz = 1 << __lg(2 * (n + m - 1) - 1);
l.resize(sz), FMT<mod>(l);
r.resize(sz), FMT<mod>(r);
rep(i, sz) l[i] *= r[i];
FMT<mod>(l, true);
l.resize(n + m - 1);
}
Poly operator*(const Poly &l, const Poly &r) {
if(l.empty() or r.empty()) return Poly();
int n = size(l), m = size(r), sz = 1 << __lg(2 * (n + m - 1) - 1);
vector<M0> l0(n), r0(m);
vector<M1> l1(n), r1(m);
vector<M2> l2(n), r2(m);
rep(i, n) l0[i] = l[i].a, l1[i] = l[i].a, l2[i] = l[i].a;
rep(i, m) r0[i] = r[i].a, r1[i] = r[i].a, r2[i] = r[i].a;
mul<mod0>(l0, r0), mul<mod1>(l1, r1), mul<mod2>(l2, r2);
Poly res(n + m - 1);
// garner
static constexpr M1 inv0 = 613999507;
static constexpr M2 inv1 = 1147332803, inv0m1 = 45381342;
static constexpr mint m0 = mod0, m0m1 = m0 * mod1;
rep(i, n + m - 1) {
int y0 = l0[i].a;
int y1 = (inv0 * (l1[i] - y0)).a;
int y2 = (inv0m1 * (l2[i] - y0) - inv1 * y1).a;
res[i] = m0 * y1 + m0m1 * y2 + y0;
}
return res;
}
Poly &operator*=(Poly &l, const Poly &r) { return l = l * r; }
ostream &operator<<(ostream &os, Poly a) {
for(auto e : a) cout << e.a << " ";
return os;
}
} // namespace modular
using namespace modular;
template <typename G = Graph> struct SCC {
G g;
Graph rg;
vector<int> comp, ord;
vector<bool> used;
int num; // 連結成分の数
SCC(G &g) : g(g), rg(g.size()), comp(g.size(), -1), used(g.size()) {
rep(i, g.size()) for(auto &e : g[i]) rg[e].emplace_back(i);
ord.reserve(g.size());
build();
};
SCC(int n) : g(n), rg(n), comp(n, -1), used(n) { ord.reserve(n); };
inline void add(int a, int b) {
g[a].emplace_back(b);
rg[b].emplace_back(a);
}
int operator[](int k) { return comp[k]; }
void dfs(int x) {
if(used[x]) return;
used[x] = true;
for(auto &e : g[x])
if(!used[e]) dfs(e);
ord.emplace_back(x);
}
void rdfs(int x, int cnt) {
if(comp[x] != -1) return;
comp[x] = cnt;
for(int &e : rg[x])
if(comp[e] == -1) rdfs(e, cnt);
}
void build() {
rep(i, g.size()) dfs(i);
reverse(all(ord));
num = 0;
for(int &i : ord)
if(comp[i] == -1) { rdfs(i, num), num++; }
}
// 強連結成分を潰した DAG を返す
Graph getGraph() {
Graph res(num);
rep(i, g.size()) {
for(auto &e : g[i]) {
if(comp[e] == comp[i]) continue;
res[comp[i]].emplace_back(comp[e]);
}
}
rep(i, g.size()) UNIQUE(res[i]);
return res;
}
// 強連結成分ごとに属する頂点を返す
vector<vector<int>> belong() {
vector<vector<int>> res(num);
rep(i, g.size()) res[comp[i]].emplace_back(i);
return res;
}
};
struct TwoSat : SCC<Graph> {
int n;
using SCC::SCC;
TwoSat(int n) : n(n), SCC(n * 2) {}
// not i = i + n
inline int rev(int x) { return x >= n ? x - n : x + n; }
inline int id(int x) { return x < 0 ? n - x - 1 : x - 1; }
inline void IF(int x, int y) {
// x => y
add(x, y), add(rev(y), rev(x));
}
void OR(int x, int y) { IF(rev(id(x)), id(y)); }
vector<int> solve() {
build();
vector<int> res(n);
rep(i, n) {
if(comp[i] == comp[rev(i)]) return vector<int>();
res[i] = comp[i] > comp[rev(i)];
}
return res;
}
bool can() {
build();
rep(i, n) {
if(comp[i] == comp[rev(i)]) return false;
}
return true;
}
};
template <typename T = int> struct UnionFind {
vector<int> data;
vector<T> sz;
bool is_default;
UnionFind(int n) {
data.assign(n, -1);
sz.assign(n, 1);
is_default = true;
}
UnionFind(int n, vector<T> &a) {
data.assign(n, -1);
sz = a;
is_default = false;
}
bool unite(int x, int y) {
x = find(x), y = find(y);
if(x == y) return false;
if(data[x] > data[y]) swap(x, y);
data[x] += data[y];
if(!is_default) sz[x] += sz[y];
data[y] = x;
return true;
}
bool same(int x, int y) { return find(x) == find(y); }
int find(int x) {
if(data[x] < 0) return x;
return (data[x] = find(data[x]));
}
T size(int x) { return (is_default ? -data[find(x)] : sz[find(x)]); }
};
main() {
INT(n, m);
vi l(m), r(m), p(n);
rep(i, m) cin >> l[i] >> r[i] >> p[i], l[i]--;
vi imos(n + 1);
rep(i, m) if(p[i]) imos[l[i]]++, imos[r[i]]--;
rep(i, n) imos[i + 1] += imos[i];
SegmentTree<mint> seg(
n + 1, [](mint x, mint y) { return x + y; }, (mint)0);
seg.set(0, 1);
vv(pii, query, n + 1);
rep(i, m) query[r[i] - 1].eb(l[i], p[i]);
mint P = 1;
seg.build();
int L = 0;
rep(i, n) {
if(!imos[i]) { seg.update(i + 1, seg.query(0, i + 1) * inv(2)); }
for(auto [a, b] : query[i]) {
if(!b)
while(L <= a) seg.update(L++, 0);
}
}
mint ans = seg.query(0, n + 1);
UnionFind uf((n + 1) * 2);
rep(i, m) {
if(p[i] == 1) {
uf.unite(r[i], l[i]);
uf.unite(r[i] + n + 1, l[i] + n + 1);
} else if(p[i] == -1) {
uf.unite(r[i], l[i] + n + 1);
uf.unite(r[i] + n + 1, l[i]);
}
}
bool can = true;
rep(i, n + 1) {
if(uf.same(i, i + n + 1)) can = false;
}
if(!can) {
cout << 0 << endl;
} else {
int cnt = 0;
rep(i, n + 1) if(uf.find(i) == i) cnt++;
rep(i, n + 1) if(uf.find(i + n + 1) == i + n + 1) cnt++;
ans *= modpow(2, cnt / 2);
ans *= inv(2);
cout << ans << endl;
}
}