// #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 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=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 using V = vector; template using VV = vector>; template bool chmax(T& x, U y){ if(x bool chmin(T& x, U y){ if(y void mkuni(V& v){sort(all(v));v.erase(unique(all(v)),v.end());} template int lwb(const V& v, const T& a){return lower_bound(all(v),a) - v.begin();} template V Vec(size_t a) { return V(a); } template auto Vec(size_t a, Ts... ts) { return V(ts...))>(a, Vec(ts...)); } template ostream& operator<<(ostream& o,const pair &p){ return o<<"("< void print_tuple_impl(ostream& os, const Tuple& tup, index_sequence){ ((os << (Is == 0 ? "" : ",") << get(tup)), ...); } template std::ostream& operator<<(std::ostream& os, const std::tuple& tup) { os << "("; print_tuple_impl(os, tup, std::index_sequence_for{}); os << ")"; return os; } template ostream& operator<<(ostream& o,const vector &vc){ o<<"{"; for(const T& v:vc) o< D divFloor(D a, D b){ return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0); } template 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 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 [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 friend ModInt operator+(T a, const ModInt& b){ return (ModInt(a) += b);} template friend ModInt operator-(T a, const ModInt& b){ return (ModInt(a) -= b);} template friend ModInt operator*(T a, const ModInt& b){ return (ModInt(a) *= b);} template 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>(istream &i, ModInt& x){ ll v; i >> v; x = ModInt(v); return i; } friend ostream& operator<<(ostream &o, const ModInt& x){ return o<; //using mint = ModInt<1000000007>; V fact,ifact,invs; // a,b >= 0 のみ mint Choose(int a,int b){ if(b<0 || a= 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=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 void hadamard(V& a, bool inv = false){ int n = si(a); assert(__builtin_popcount(n) == 1); for(int i=1;i vector hadamard2(const vector& a, const vector& b){ assert(a.size() == b.size()); int n = si(a); assert(__builtin_popcount(n) == 1); vector> c(n); rep(i,n) c[i] = {a[i], b[i]}; for(int i=1;i 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> 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 f(1< 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'; }