use std::io::Write; fn main() { input! { n: usize, m: usize, p: [(usize, usize); m], } let p = p.into_iter().map(|p| (p.0, p.1 + 1)).collect::>(); let ans = fast(n, &p); let out = std::io::stdout(); let mut out = std::io::BufWriter::new(out.lock()); for a in ans.iter() { writeln!(out, "{}", *a).ok(); } } fn fast(n: usize, p: &[(usize, usize)]) -> Vec { if p.iter().any(|p| *p == (0, 1 << n)) { let prod = p.iter().fold(M::one(), |s, a| s * M::from(a.1 - a.0)); return vec![prod * M::new(1 << n).inv(); 1 << n]; } let mut q = Vec::from(p); let mut ans = vec![M::zero(); 1 << n]; for i in 0..n { let mut dp = vec![M::zero(); 2 << (n - i)]; for dp in dp.chunks_exact_mut(4) { dp[0] = M::one(); } fwht(&mut dp[..2]); for dp in dp.chunks_exact_mut(4).skip(1) { fwht(dp); } let mut xor = 0; for (&(l, r), (ref mut s, ref mut t)) in p.iter().zip(q.iter_mut()) { xor ^= l & !((2 << i) - 1); let pos = if r == 1 << n { 0 } else { (l ^ r) >> (i + 1) }; let mut ep = [M::zero(); 4]; if l < *s { ep[l >> i & 1] += M::from(*s - l); } if *s < *t && *s >> i & 1 == 1 { ep[1] += M::new(1 << i); *s += 1 << i; } let up = if pos > 0 { 2 } else { 0 }; if *t < r { ep[up + (r >> i & 1)] += M::from(r - *t); } if *s < *t && *t >> i & 1 == 1 { *t -= 1 << i; ep[up] += M::new(1 << i); } let dp = &mut dp[(4 * pos)..(4 * pos + 4)]; if pos == 0 { fwht(&mut ep[..2]); dp[..2].dot_assign(&ep[..2]); } else { fwht(&mut ep); dp.dot_assign(&ep); } } let mut size = 4; while size < dp.len() { for dp in dp.chunks_exact_mut(2 * size) { let (l, r) = dp.split_at_mut(size); let (a, b) = l.split_at_mut(size / 2); let (c, d) = r.split_at_mut(size / 2); let ab = a.iter_mut().zip(b.iter_mut()); let cd = c.iter_mut().zip(d.iter_mut()); for ((a, b), (c, d)) in ab.zip(cd) { let x = *a * *c; let y = *a * *d; let z = *b * *d; let w = *b * *c; *a = x; *b = y; *c = z; *d = w; } } size *= 2; } dp.truncate(1 << (n - i)); fwht(&mut dp); let inv = M::from(dp.len()).inv(); for dp in dp.iter_mut() { *dp *= inv; } let invi = M::new(1 << i).inv(); for (j, &val) in dp.iter().enumerate() { let s = xor ^ (j << i); let t = s + (1 << i); let sum = ans[s..t].iter().fold(M::zero(), |s, a| s + *a); let add = (val - sum) * invi; for a in ans[s..t].iter_mut() { *a += add; } } } ans } fn fwht(a: &mut [T]) where T: std::ops::Add + std::ops::Sub + Copy, { bitwise_transform(a, |a, b| { let x = *a + *b; let y = *a - *b; *a = x; *b = y; }); } type M = ModInt<998244353>; // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 #[macro_export] macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } #[macro_export] macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } #[macro_export] macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- use std::ops::*; // ---------- begin trait ---------- pub trait Zero: Sized + Add { fn zero() -> Self; fn is_zero(&self) -> bool; } pub trait One: Sized + Mul { fn one() -> Self; fn is_one(&self) -> bool; } pub trait SemiRing: Zero + One {} pub trait Ring: SemiRing + Sub + Neg {} pub trait Field: Ring + Div {} impl SemiRing for T where T: Zero + One {} impl Ring for T where T: SemiRing + Sub + Neg {} impl Field for T where T: Ring + Div {} // ---------- end trait ---------- // ---------- begin modint ---------- pub const fn pow_mod(mut r: u32, mut n: u32, m: u32) -> u32 { let mut t = 1; while n > 0 { if n & 1 == 1 { t = (t as u64 * r as u64 % m as u64) as u32; } r = (r as u64 * r as u64 % m as u64) as u32; n >>= 1; } t } pub const fn primitive_root(p: u32) -> u32 { let mut m = p - 1; let mut f = [1; 30]; let mut k = 0; let mut d = 2; while d * d <= m { if m % d == 0 { f[k] = d; k += 1; } while m % d == 0 { m /= d; } d += 1; } if m > 1 { f[k] = m; k += 1; } let mut g = 1; while g < p { let mut ok = true; let mut i = 0; while i < k { ok &= pow_mod(g, (p - 1) / f[i], p) > 1; i += 1; } if ok { break; } g += 1; } g } pub const fn is_prime(n: u32) -> bool { if n <= 1 { return false; } let mut d = 2; while d * d <= n { if n % d == 0 { return false; } d += 1; } true } #[derive(Clone, Copy, PartialEq, Eq)] pub struct ModInt(u32); impl ModInt<{ M }> { const REM: u32 = { let mut t = 1u32; let mut s = !M + 1; let mut n = !0u32 >> 2; while n > 0 { if n & 1 == 1 { t = t.wrapping_mul(s); } s = s.wrapping_mul(s); n >>= 1; } t }; const INI: u64 = ((1u128 << 64) % M as u128) as u64; const IS_PRIME: () = assert!(is_prime(M)); const fn reduce(x: u64) -> u32 { let _ = Self::IS_PRIME; let b = (x as u32 * Self::REM) as u64; let t = x + b * M as u64; let mut c = (t >> 32) as u32; if c >= M { c -= M; } c as u32 } const fn multiply(a: u32, b: u32) -> u32 { Self::reduce(a as u64 * b as u64) } pub const fn new(v: u32) -> Self { assert!(v < M); Self(Self::reduce(v as u64 * Self::INI)) } pub const fn const_mul(&self, rhs: Self) -> Self { Self(Self::multiply(self.0, rhs.0)) } pub const fn pow(&self, mut n: u64) -> Self { let mut t = Self::new(1); let mut r = *self; while n > 0 { if n & 1 == 1 { t = t.const_mul(r); } r = r.const_mul(r); n >>= 1; } t } pub const fn inv(&self) -> Self { assert!(self.0 != 0); self.pow(M as u64 - 2) } pub const fn get(&self) -> u32 { Self::reduce(self.0 as u64) } pub const fn zero() -> Self { Self::new(0) } pub const fn one() -> Self { Self::new(1) } } impl Add for ModInt<{ M }> { type Output = Self; fn add(self, rhs: Self) -> Self::Output { let mut v = self.0 + rhs.0; if v >= M { v -= M; } Self(v) } } impl Sub for ModInt<{ M }> { type Output = Self; fn sub(self, rhs: Self) -> Self::Output { let mut v = self.0 - rhs.0; if self.0 < rhs.0 { v += M; } Self(v) } } impl Mul for ModInt<{ M }> { type Output = Self; fn mul(self, rhs: Self) -> Self::Output { self.const_mul(rhs) } } impl Div for ModInt<{ M }> { type Output = Self; fn div(self, rhs: Self) -> Self::Output { self * rhs.inv() } } impl AddAssign for ModInt<{ M }> { fn add_assign(&mut self, rhs: Self) { *self = *self + rhs; } } impl SubAssign for ModInt<{ M }> { fn sub_assign(&mut self, rhs: Self) { *self = *self - rhs; } } impl MulAssign for ModInt<{ M }> { fn mul_assign(&mut self, rhs: Self) { *self = *self * rhs; } } impl DivAssign for ModInt<{ M }> { fn div_assign(&mut self, rhs: Self) { *self = *self / rhs; } } impl Neg for ModInt<{ M }> { type Output = Self; fn neg(self) -> Self::Output { if self.0 == 0 { self } else { Self(M - self.0) } } } impl std::fmt::Display for ModInt<{ M }> { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.get()) } } impl std::fmt::Debug for ModInt<{ M }> { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.get()) } } impl std::str::FromStr for ModInt<{ M }> { type Err = std::num::ParseIntError; fn from_str(s: &str) -> Result { let val = s.parse::()?; Ok(ModInt::new(val)) } } impl From for ModInt<{ M }> { fn from(val: usize) -> ModInt<{ M }> { ModInt::new((val % M as usize) as u32) } } // ---------- end modint ---------- // ---------- begin precalc ---------- pub struct Precalc { fact: Vec>, ifact: Vec>, inv: Vec>, } impl Precalc { pub fn new(size: usize) -> Self { let mut fact = vec![ModInt::one(); size + 1]; let mut ifact = vec![ModInt::one(); size + 1]; let mut inv = vec![ModInt::one(); size + 1]; for i in 2..=size { fact[i] = fact[i - 1] * ModInt::from(i); } ifact[size] = fact[size].inv(); for i in (2..=size).rev() { inv[i] = ifact[i] * fact[i - 1]; ifact[i - 1] = ifact[i] * ModInt::from(i); } Self { fact, ifact, inv } } pub fn fact(&self, n: usize) -> ModInt { self.fact[n] } pub fn ifact(&self, n: usize) -> ModInt { self.ifact[n] } pub fn inv(&self, n: usize) -> ModInt { assert!(0 < n); self.inv[n] } pub fn perm(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[n - k] } pub fn binom(&self, n: usize, k: usize) -> ModInt { if n < k { return ModInt::zero(); } self.fact[n] * self.ifact[k] * self.ifact[n - k] } } // ---------- end precalc ---------- impl Zero for ModInt<{ M }> { fn zero() -> Self { Self::zero() } fn is_zero(&self) -> bool { self.0 == 0 } } impl One for ModInt<{ M }> { fn one() -> Self { Self::one() } fn is_one(&self) -> bool { self.get() == 1 } } // ---------- begin array op ---------- pub trait ArrayAdd { type Item; fn add(&self, rhs: &[Self::Item]) -> Vec; } impl ArrayAdd for [T] where T: Zero + Copy, { type Item = T; fn add(&self, rhs: &[Self::Item]) -> Vec { let mut c = vec![T::zero(); self.len().max(rhs.len())]; c[..self.len()].copy_from_slice(self); c.add_assign(rhs); c } } pub trait ArrayAddAssign { type Item; fn add_assign(&mut self, rhs: &[Self::Item]); } impl ArrayAddAssign for [T] where T: Add + Copy, { type Item = T; fn add_assign(&mut self, rhs: &[Self::Item]) { assert!(self.len() >= rhs.len()); self.iter_mut().zip(rhs).for_each(|(x, a)| *x = *x + *a); } } impl ArrayAddAssign for Vec where T: Zero + Add + Copy, { type Item = T; fn add_assign(&mut self, rhs: &[Self::Item]) { if self.len() < rhs.len() { self.resize(rhs.len(), T::zero()); } self.as_mut_slice().add_assign(rhs); } } pub trait ArraySub { type Item; fn sub(&self, rhs: &[Self::Item]) -> Vec; } impl ArraySub for [T] where T: Zero + Sub + Copy, { type Item = T; fn sub(&self, rhs: &[Self::Item]) -> Vec { let mut c = vec![T::zero(); self.len().max(rhs.len())]; c[..self.len()].copy_from_slice(self); c.sub_assign(rhs); c } } pub trait ArraySubAssign { type Item; fn sub_assign(&mut self, rhs: &[Self::Item]); } impl ArraySubAssign for [T] where T: Sub + Copy, { type Item = T; fn sub_assign(&mut self, rhs: &[Self::Item]) { assert!(self.len() >= rhs.len()); self.iter_mut().zip(rhs).for_each(|(x, a)| *x = *x - *a); } } impl ArraySubAssign for Vec where T: Zero + Sub + Copy, { type Item = T; fn sub_assign(&mut self, rhs: &[Self::Item]) { if self.len() < rhs.len() { self.resize(rhs.len(), T::zero()); } self.as_mut_slice().sub_assign(rhs); } } pub trait ArrayDot { type Item; fn dot(&self, rhs: &[Self::Item]) -> Vec; } impl ArrayDot for [T] where T: Mul + Copy, { type Item = T; fn dot(&self, rhs: &[Self::Item]) -> Vec { assert!(self.len() == rhs.len()); self.iter().zip(rhs).map(|p| *p.0 * *p.1).collect() } } pub trait ArrayDotAssign { type Item; fn dot_assign(&mut self, rhs: &[Self::Item]); } impl ArrayDotAssign for [T] where T: MulAssign + Copy, { type Item = T; fn dot_assign(&mut self, rhs: &[Self::Item]) { assert!(self.len() == rhs.len()); self.iter_mut().zip(rhs).for_each(|(x, a)| *x *= *a); } } // ---------- end array op ---------- pub fn bitwise_transform(a: &mut [T], f: F) where F: Fn(&mut T, &mut T), { let size = a.len(); assert!(size > 0 && size.next_power_of_two() == size); let n = size.trailing_zeros(); for i in 0..n { let w = 1 << i; for a in a.chunks_exact_mut(2 * w) { let (l, r) = a.split_at_mut(w); for (l, r) in l.iter_mut().zip(r.iter_mut()) { f(l, r); } } } }