#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template ostream &operator<<(ostream &os, const vector &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; } template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } #define COLOR(s) ("\x1b[" s "m") //////////////////////////////////////////////////////////////////////////////// template struct ModInt { static constexpr unsigned M = M_; unsigned x; constexpr ModInt() : x(0U) {} constexpr ModInt(unsigned x_) : x(x_ % M) {} constexpr ModInt(unsigned long long x_) : x(x_ % M) {} constexpr ModInt(int x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} constexpr ModInt(long long x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; } ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; } ModInt &operator*=(const ModInt &a) { x = (static_cast(x) * a.x) % M; return *this; } ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); } ModInt pow(long long e) const { if (e < 0) return inv().pow(-e); ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b; } ModInt inv() const { unsigned a = M, b = x; int y = 0, z = 1; for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast(q) * z; y = z; z = w; } assert(a == 1U); return ModInt(y); } ModInt operator+() const { return *this; } ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; } ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); } ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); } ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); } ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); } 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); } explicit operator bool() const { return x; } bool operator==(const ModInt &a) const { return (x == a.x); } bool operator!=(const ModInt &a) const { return (x != a.x); } friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; } }; //////////////////////////////////////////////////////////////////////////////// constexpr unsigned MO = 998244353; using Mint = ModInt; // \prod (a0 x^p0 + a1 x^p1) struct XorConvolve2Terms { int n; int base; vector fss[2]; XorConvolve2Terms() {} XorConvolve2Terms(int n_) : n(n_), base(0) { for (int u = 0; u < 2; ++u) fss[u].assign(1 << n, 1); } void add(int p0, int p1, Mint a0, Mint a1) { base ^= p0; fss[0][p0 ^ p1] *= (a0 + a1); fss[1][p0 ^ p1] *= (a0 - a1); } vector run() { // *= fss[u][p] when |p \cap (higher bits)| == u (mod 2) for (int e = 0; e < n; ++e) { for (int o = 0; o < 1 << n; o += (1 << (e + 1))) for (int p0 = o; p0 < o + (1 << e); ++p0) { const int p1 = p0 | 1 << e; const Mint t00 = fss[0][p0]; const Mint t01 = fss[0][p1]; const Mint t10 = fss[1][p0]; const Mint t11 = fss[1][p1]; fss[0][p0] = t00 * t01; fss[0][p1] = t00 * t11; fss[1][p0] = t10 * t11; fss[1][p1] = t10 * t01; } } auto &fs = fss[0]; for (int e = 0; e < n; ++e) { for (int o = 0; o < 1 << n; o += (1 << (e + 1))) for (int p0 = o; p0 < o + (1 << e); ++p0) { const int p1 = p0 | 1 << e; const Mint t0 = fs[p0]; const Mint t1 = fs[p1]; fs[p0] = t0 + t1; fs[p1] = t0 - t1; } } const Mint invTwo = Mint(1 << n).inv(); for (int p = 0; p < 1 << n; ++p) fs[p] *= invTwo; for (int p = 0; p < 1 << n; ++p) if (p < (base ^ p)) swap(fs[p], fs[base ^ p]); return fs; } }; vector xorConvolveIntervalsLR(int n, const vector &ls, const vector &rs) { const int E = n; const int N = ls.size(); const auto &A = ls; const auto &B = rs; // Mint ans = 0; vector ans(1 << E, 0); for (int e = 0; e < E; ++e) { // free bits: [0, e) const int mask = (1 << e) - 1; const int m = E - 1 - e; // Mint way = 0; vector way(1 << (m + 1), 0); for (int phase = 0; phase < 2; ++phase) { // phase = 1: do not choose interval to make free b bits // mod (z^2 - 1) for (const int z : {+1, -1}) { // (high, weight) 2-taku XorConvolve2Terms f(m); for (int i = 0; i < N; ++i) { const int hb = B[i] >> (e + 1); const int ha = A[i] >> (e + 1); Mint wb = +Mint(B[i] & mask) * ((B[i] >> e & 1) ? z : 1); Mint wa = -Mint(A[i] & mask) * ((A[i] >> e & 1) ? z : 1); if (phase == 0) { if (B[i] >> e & 1) wb += +Mint(1 << e); if (A[i] >> e & 1) wa += -Mint(1 << e); } f.add(hb, ha, wb, wa); } // way += (phase ? -1 : +1) * f.run()[0]; const auto res = f.run(); for (int h = 0; h < 1 << m; ++h) { way[h << 1] += (phase ? -1 : +1) * res[h]; way[h << 1 | 1] += (phase ? -1 : +1) * z * res[h]; } } } // way /= 2; // way /= (1 << e); // ans += way; const Mint coef = Mint(2).pow(-(1 + e)); for (int h = 0; h < 1 << E; ++h) ans[h] += coef * way[h >> e]; } return {ans}; } int N, M; vector L, R; int main() { for (; ~scanf("%d%d", &N, &M); ) { L.resize(M); R.resize(M); for (int i = 0; i < M; ++i) { scanf("%d%d", &L[i], &R[i]); ++R[i]; } const auto ans = xorConvolveIntervalsLR(N + 1, L, R); for (int h = 0; h < 1 << N; ++h) { printf("%u\n", ans[h].x); } } return 0; } // library kakikake...