結果

問題 No.2990 Interval XOR
ユーザー sigma425
提出日時 2025-04-23 02:48:20
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 253 ms / 2,000 ms
コード長 8,886 bytes
コンパイル時間 4,109 ms
コンパイル使用メモリ 286,632 KB
実行使用メモリ 19,072 KB
最終ジャッジ日時 2025-04-23 02:48:34
合計ジャッジ時間 13,654 ms
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 * 3
other AC * 37
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ソースコード

diff # 

// #line 1 "2990.cpp"
/*
	Interval XOR
	i = (2h+1) * 2^s として 各 s について h \in [0,2^{n-1-s}) についてまとめて解く
	L = 0 なら p(h & (R>>(s+1))) * (h によらない、区間による部分) の区間に対する積になってできる
	一般には p(h & (R>>(s+1))) * c1 + p(h & (L>>(s+1))) * c2 の積 となるので和の積になってやばそうだが、
	実は意味なさそうな変形 = p(h & (R>>(s+1))) * (c1 + c2 * p(h & ((R^L)>>(s+1)))) の形ならできる
*/

// #pragma GCC target("avx2,avx512f,avx512vl,avx512bw,avx512dq,avx512cd,avx512vbmi,avx512vbmi2,avx512vpopcntdq,avx512bitalg,bmi,bmi2,lzcnt,popcnt")
// #pragma GCC optimize("Ofast")

// #line 2 "/home/sigma/comp/library/template.hpp"

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
#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 per(i,n) for(int i=int(n)-1;i>=0;i--)
#define per1(i,n) for(int i=int(n);i>0;i--)
#define all(c) c.begin(),c.end()
#define si(x) int(x.size())
#define pb push_back
#define eb emplace_back
#define fs first
#define sc second
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;
template<class T,class U> bool chmax(T& x, U y){
	if(x<y){ x=y; return true; }
	return false;
}
template<class T,class U> bool chmin(T& x, U y){
	if(y<x){ x=y; return true; }
	return false;
}
template<class T> void mkuni(V<T>& v){sort(all(v));v.erase(unique(all(v)),v.end());}
template<class T> int lwb(const V<T>& v, const T& a){return lower_bound(all(v),a) - v.begin();}
template<class T>
V<T> Vec(size_t a) {
	return V<T>(a);
}
template<class T, class... Ts>
auto Vec(size_t a, Ts... ts) {
  return V<decltype(Vec<T>(ts...))>(a, Vec<T>(ts...));
}
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
	return o<<"("<<p.fs<<","<<p.sc<<")";
}

template<typename Tuple, size_t... Is>
void print_tuple_impl(ostream& os, const Tuple& tup, index_sequence<Is...>){
	((os << (Is == 0 ? "" : ",") << get<Is>(tup)), ...);
}
template<typename... Args>
std::ostream& operator<<(std::ostream& os, const std::tuple<Args...>& tup) {
	os << "(";
	print_tuple_impl(os, tup, std::index_sequence_for<Args...>{});
	os << ")";
	return os;
}

template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
	o<<"{";
	for(const T& v:vc) o<<v<<",";
	o<<"}";
	return o;
}
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }

#ifdef LOCAL
const bool DEBUG = true;
const bool SUBMIT = false;
#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl
void dmpr(ostream& os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ~ ";
	dmpr(os,args...);
}
#define shows(...) cerr << "LINE" << __LINE__ << " : ";dmpr(cerr,##__VA_ARGS__)
#define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {";  \
	for(auto v: x) cerr << v << ","; cerr << "}" << endl;
#else
const bool DEBUG = false;
const bool SUBMIT = true;
#define show(x) void(0)
#define dump(x) void(0)
#define shows(...) void(0)
#endif

template<class D> D divFloor(D a, D b){
	return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0);
}
template<class D> D divCeil(D a, D b) {
	return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0);
}
// #line 1 "/home/sigma/comp/library/math/mint.hpp"
template<unsigned int mod_>
struct ModInt{	
	using uint = unsigned int;
	using ll = long long;
	using ull = unsigned long long;

	constexpr static uint mod = mod_;

	uint v;
	ModInt():v(0){}
	ModInt(ll _v):v(normS(_v%mod+mod)){}
	explicit operator bool() const {return v!=0;}
	static uint normS(const uint &x){return (x<mod)?x:x-mod;}		// [0 , 2*mod-1] -> [0 , mod-1]
	static ModInt make(const uint &x){ModInt m; m.v=x; return m;}
	ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));}
	ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));}
	ModInt operator-() const { return make(normS(mod-v)); }
	ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);}
	ModInt operator/(const ModInt& b) const { return *this*b.inv();}
	ModInt& operator+=(const ModInt& b){ return *this=*this+b;}
	ModInt& operator-=(const ModInt& b){ return *this=*this-b;}
	ModInt& operator*=(const ModInt& b){ return *this=*this*b;}
	ModInt& operator/=(const ModInt& b){ return *this=*this/b;}
	ModInt& operator++(int){ return *this=*this+1;}
	ModInt& operator--(int){ return *this=*this-1;}
	template<class T> friend ModInt operator+(T a, const ModInt& b){ return (ModInt(a) += b);}
	template<class T> friend ModInt operator-(T a, const ModInt& b){ return (ModInt(a) -= b);}
	template<class T> friend ModInt operator*(T a, const ModInt& b){ return (ModInt(a) *= b);}
	template<class T> friend ModInt operator/(T a, const ModInt& b){ return (ModInt(a) /= b);}
	ModInt pow(ll p) const {
		if(p<0) return inv().pow(-p);
		ModInt a = 1;
		ModInt x = *this;
		while(p){
			if(p&1) a *= x;
			x *= x;
			p >>= 1;
		}
		return a;
	}
	ModInt inv() const {		// should be prime
		return pow(mod-2);
	}

	bool operator==(const ModInt& b) const { return v==b.v;}
	bool operator!=(const ModInt& b) const { return v!=b.v;}
	bool operator<(const ModInt& b) const { return v<b.v;}
	friend istream& operator>>(istream &i, ModInt& x){
		ll v; i >> v;
		x = ModInt(v);
		return i;
	}
	friend ostream& operator<<(ostream &o, const ModInt& x){ return o<<x.v;}
	// friend ostream& operator<<(ostream &o,const ModInt& x){
	// 	for(int b=1;b<=1000;b++){
	// 		ModInt ib = ModInt(b).inv();
	// 		for(int a=-1000;a<=1000;a++){
	// 			if(ModInt(a) * ib == x){
	// 				return o << a << "/" << b;
	// 			}
	// 		}
	// 	}
	// 	return o<<x.v;
	// }
};
using mint = ModInt<998244353>;
//using mint = ModInt<1000000007>;

V<mint> fact,ifact,invs;
// a,b >= 0 のみ
mint Choose(int a,int b){
	if(b<0 || a<b) return 0;
	return fact[a] * ifact[b] * ifact[a-b];
}

/*
// b >= 0 の範囲で、 Choose(a,b) = a(a-1)..(a-b+1) / b!
mint Choose(int a,int b){
	if(b<0 || a<b) return 0;
	return fact[a] * ifact[b] * ifact[a-b];
}
*/

void InitFact(int N){	//[0,N]
	N++;
	fact.resize(N);
	ifact.resize(N);
	invs.resize(N);
	fact[0] = 1;
	rep1(i,N-1) fact[i] = fact[i-1] * i;
	ifact[N-1] = fact[N-1].inv();
	for(int i=N-2;i>=0;i--) ifact[i] = ifact[i+1] * (i+1);
	rep1(i,N-1) invs[i] = fact[i-1] * ifact[i];
}
// #line 14 "2990.cpp"

template<class T>
void hadamard(V<T>& a, bool inv = false){
	int n = si(a);
	assert(__builtin_popcount(n) == 1);
	for(int i=1;i<n;i<<=1){
		for(int j=0;j<n;j+=i<<1){
			rep(k,i){
				T s = a[j+k], t = a[j+k+i];
				a[j+k] = s+t;
				a[j+k+i] = s-t;
			}
		}
	}
	if(inv){
		T in = T(1)/n;
		for(auto& x: a) x *= in;
	}
}
/*
	c[i] = \sum_j ( p(j & 1) == 1 ? a[i] : b[i] )

	上のコードを実行中の a に入っている値は、入力の a を使って、 + a[] + a[] - a[] - a[] 
	みたいに係数が-1,0,1 のいずれかで書けることがわかる
	ということは係数が1のa[]の和、-1のa[]の和、を分けて持てば、最終的に + なものの和と - なものの和がわかる

	T は逆元すら仮定せず可換モノイドでよい 不思議かも
	今回は T = (mint, *) なので直接書いています
*/
template<class T>
vector<T> hadamard2(const vector<T>& a, const vector<T>& b){
	assert(a.size() == b.size());
	int n = si(a);
	assert(__builtin_popcount(n) == 1);
	vector<pair<T,T>> c(n); rep(i,n) c[i] = {a[i], b[i]};
	for(int i=1;i<n;i<<=1){
		for(int j=0;j<n;j+=i<<1){
			rep(k,i){
				auto s = c[j+k], t = c[j+k+i];
				c[j+k] = {s.fs*t.fs, s.sc*t.sc};
				c[j+k+i] = {s.fs*t.sc, s.sc*t.fs};
			}
		}
	}
	vector<T> res(n); rep(i,n) res[i] = c[i].fs;
	return res;
}


int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);		//DON'T USE scanf/printf/puts !!
	cout << fixed << setprecision(20);

	int N,M; cin >> N >> M;
	vector<pair<int,int>> seg(M);
	rep(i,M) cin >> seg[i].fs >> seg[i].sc, seg[i].sc++;
	
	/*
		f[i] = 各区間 [L,R) を hadamard 変換した時の [i] の各点積
			 = \prod_{区間} \sum_{L <= j < R} p(j & i)
	*/
	V<mint> f(1<<N);

	{
		// i = 0
		f[0] = 1; for(auto [L,R] : seg) f[0] *= R-L;
	}

	rep(s,N){
		// i = (2h+1) * 2^s for h in [0,2^{N-1-s})
		const int mask = (1<<(s+1)) - 1;
		const int H = 1 << (N-1-s);
		V<mint> a(H,1), b(H,1);
		for(auto [L,R] : seg){
			/*
				\sum_{L <= j < R} p(j & (2h+1) * 2^s)
				= p(h & r) * c1 + p(h & l) * c2
				= p(h & r) * (c1 + c2 * p(h & (r^l)))
			*/
			int r = R >> (s+1), l = L >> (s+1);
			if(r == H) r = 0;
			int rm = R & mask, lm = L & mask;
			mint c1 = min(rm,(1<<(s+1))-rm), c2 = -min(lm,(1<<(s+1))-lm);
			a[r] *= 1; b[r] *= -1;
			a[r^l] *= c1 + c2; b[r^l] *= c1 - c2;
		}
		auto c = hadamard2(a,b);
		rep(h,H) f[(2*h+1) << s] = c[h];
	}
	hadamard(f);
	mint ip2 = mint(2).pow(-N);
	for(auto& v: f) cout << v * ip2 << '\n';
}
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