fn main() { let mut io = IO::new(); input!{ from io, k: i64, n: usize } let l = atkin_sieve(n).into_iter().filter(|&v| v >= k).map(|v| v as usize).collect::>(); let mut ans = l[0]; let mut mx = 1; let mut j = 0; let m = l.len(); let mut count = vec![0; 10]; for i in 0..m { while j < m && count[l[j] % 9] == 0 { count[l[j] % 9] += 1; j += 1; } if j - i >= mx { mx = j - i; ans = l[i]; } count[l[i] % 9] -= 1; } io.println(ans); } pub fn atkin_sieve(n: usize) -> Vec { let mut sieve = BitSet::new(n+1); let lim = (n as f64).sqrt() as usize + 1; for z in (1..6).step_by(4) { for y in (z..lim).step_by(6) { for x in 1..lim { if 4 * x * x + y * y > n { break; } sieve.flip(4 * x * x + y * y); } for x in (y+1..lim).step_by(2) { if 3 * x * x - y * y > n { break; } sieve.flip(3 * x * x - y * y); } } } for z in (2..5).step_by(2) { for y in (z..lim).step_by(6) { for x in (1..lim).step_by(2) { if 3 * x * x + y * y > n { break; } sieve.flip(3 * x * x + y * y); } for x in (y+1..lim).step_by(2) { if 3 * x * x - y * y > n { break; } sieve.flip(3 * x * x - y * y); } } } for z in 1..3 { for y in (3..lim).step_by(6) { for x in (z..lim).step_by(3) { if 4 * x * x + y * y > n { break; } sieve.flip(4 * x * x + y * y); } } } for i in 5..lim { if sieve.access(i) { for j in (i*i..n+1).step_by(i*i) { sieve.set(j, false); } } } sieve.set(2, true); sieve.set(3, true); sieve.collect().into_iter().map(|x| x as i64).collect() } use std::ops::{Shl, Shr, BitAnd, BitOr, BitXor, Not}; #[derive(Clone)] pub struct BitSet { data: Vec, size: usize } impl BitSet { pub fn new(size: usize) -> Self { let data = vec![0; (size >> 5) + 1]; BitSet{ data, size } } pub fn fill(&mut self) { self.data.iter_mut().for_each(|x| *x = 0xffffffff ); } pub fn access(&self, pos: usize) -> bool { (self.data[pos >> 5] >> (pos & 31)) & 1 == 1 } pub fn set(&mut self, pos: usize, v: bool) { if v { self.data[pos >> 5] |= 1 << (pos & 31); } else { self.data[pos >> 5] &= !(1 << (pos & 31)); } } pub fn flip(&mut self, pos: usize) { self.data[pos >> 5] ^= 1 << (pos & 31); } pub fn collect(&self) -> Vec { (0..self.size) .filter(|&i| self.access(i)) .map(|x| x as u64) .collect::>() } fn resize(&mut self, l: usize) { if self.size > l { return; } self.data.resize((l >> 5) + 1, 0); self.size = l; } } impl BitAnd for BitSet { type Output = Self; fn bitand(mut self, rhs: Self) -> Self { let m = std::cmp::max(self.size, rhs.size); self.resize(m); for (u, v) in self.data.iter_mut().zip(rhs.data.iter()) { *u &= v; } self } } impl BitOr for BitSet { type Output = Self; fn bitor(mut self, rhs: Self) -> Self { let m = std::cmp::max(self.size, rhs.size); self.resize(m); for (u, v) in self.data.iter_mut().zip(rhs.data.iter()) { *u |= v; } self } } impl BitXor for BitSet { type Output = Self; fn bitxor(mut self, rhs: Self) -> Self { let m = std::cmp::max(self.size, rhs.size); self.resize(m); for (u, v) in self.data.iter_mut().zip(rhs.data.iter()) { *u ^= v; } self } } impl Not for BitSet { type Output = Self; fn not(mut self) -> Self { for u in self.data.iter_mut() { *u = !*u; } self } } impl Shr for BitSet { type Output = Self; fn shr(mut self, rhs: usize) -> Self::Output { let big = rhs >> 5; let sml = (rhs & 31) as u32; let mask = (1 << sml) - 1; for i in 0..self.data.len() { self.data[i] = if i + big < self.data.len() { self.data[i+big] } else { 0 }; } let mut r = 0; for i in (0..self.data.len()).rev() { let u = self.data[i]; self.data[i] = (u & !mask | r).rotate_right(sml); r = u & mask; } self } } impl Shl for BitSet { type Output = Self; fn shl(mut self, rhs: usize) -> Self::Output { let n = self.data.len(); let big = rhs >> 5; let sml = (rhs & 31) as u32; let mask = (1 << sml) - 1; for i in (0..n).rev() { self.data[i] = if i >= big { self.data[i-big] } else { 0 }; } let mut r = 0; for i in 0..n { let u = self.data[i].rotate_left(sml); self.data[i] = u & !mask | r; r = u & mask; } self.data[n-1] &= (1 << (self.size & 31)) - 1; self } } // ------------ io module start ------------ use std::io::{stdout, BufWriter, Read, StdoutLock, Write}; pub struct IO { iter: std::str::SplitAsciiWhitespace<'static>, buf: BufWriter>, } impl IO { pub fn new() -> Self { let mut input = String::new(); std::io::stdin().read_to_string(&mut input).unwrap(); let input = Box::leak(input.into_boxed_str()); let out = Box::new(stdout()); IO { iter: input.split_ascii_whitespace(), buf: BufWriter::new(Box::leak(out).lock()), } } fn scan_str(&mut self) -> &'static str { self.iter.next().unwrap() } pub fn scan(&mut self) -> ::Output { ::scan(self) } pub fn scan_vec(&mut self, n: usize) -> Vec<::Output> { (0..n).map(|_| self.scan::()).collect() } pub fn print(&mut self, x: T) { ::print(self, x); } pub fn println(&mut self, x: T) { self.print(x); self.print("\n"); } pub fn iterln>(&mut self, mut iter: I, delim: &str) { if let Some(v) = iter.next() { self.print(v); for v in iter { self.print(delim); self.print(v); } } self.print("\n"); } pub fn flush(&mut self) { self.buf.flush().unwrap(); } } impl Default for IO { fn default() -> Self { Self::new() } } pub trait Scan { type Output; fn scan(io: &mut IO) -> Self::Output; } macro_rules! impl_scan { ($($t:tt),*) => { $( impl Scan for $t { type Output = Self; fn scan(s: &mut IO) -> Self::Output { s.scan_str().parse().unwrap() } } )* }; } impl_scan!(i16, i32, i64, isize, u16, u32, u64, usize, String, f32, f64); impl Scan for char { type Output = char; fn scan(s: &mut IO) -> Self::Output { s.scan_str().chars().next().unwrap() } } pub enum Bytes {} impl Scan for Bytes { type Output = &'static [u8]; fn scan(s: &mut IO) -> Self::Output { s.scan_str().as_bytes() } } pub enum Chars {} impl Scan for Chars { type Output = Vec; fn scan(s: &mut IO) -> Self::Output { s.scan_str().chars().collect() } } pub enum Usize1 {} impl Scan for Usize1 { type Output = usize; fn scan(s: &mut IO) -> Self::Output { s.scan::().wrapping_sub(1) } } impl Scan for (T, U) { type Output = (T::Output, U::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s)) } } impl Scan for (T, U, V) { type Output = (T::Output, U::Output, V::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s), V::scan(s)) } } impl Scan for (T, U, V, W) { type Output = (T::Output, U::Output, V::Output, W::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s), V::scan(s), W::scan(s)) } } pub trait Print { fn print(w: &mut IO, x: Self); } macro_rules! impl_print_int { ($($t:ty),*) => { $( impl Print for $t { fn print(w: &mut IO, x: Self) { w.buf.write_all(x.to_string().as_bytes()).unwrap(); } } )* }; } impl_print_int!(i16, i32, i64, isize, u16, u32, u64, usize, f32, f64); impl Print for u8 { fn print(w: &mut IO, x: Self) { w.buf.write_all(&[x]).unwrap(); } } impl Print for &[u8] { fn print(w: &mut IO, x: Self) { w.buf.write_all(x).unwrap(); } } impl Print for &str { fn print(w: &mut IO, x: Self) { w.print(x.as_bytes()); } } impl Print for String { fn print(w: &mut IO, x: Self) { w.print(x.as_bytes()); } } impl Print for (T, U) { fn print(w: &mut IO, (x, y): Self) { w.print(x); w.print(" "); w.print(y); } } impl Print for (T, U, V) { fn print(w: &mut IO, (x, y, z): Self) { w.print(x); w.print(" "); w.print(y); w.print(" "); w.print(z); } } mod neboccoio_macro { #[macro_export] macro_rules! input { (@start $io:tt @read @rest) => {}; (@start $io:tt @read @rest, $($rest: tt)*) => { input!(@start $io @read @rest $($rest)*) }; (@start $io:tt @read @rest mut $($rest:tt)*) => { input!(@start $io @read @mut [mut] @rest $($rest)*) }; (@start $io:tt @read @rest $($rest:tt)*) => { input!(@start $io @read @mut [] @rest $($rest)*) }; (@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [[$kind:tt; $len1:expr]; $len2:expr] $($rest:tt)*) => { let $($mut)* $var = (0..$len2).map(|_| $io.scan_vec::<$kind>($len1)).collect::>>(); input!(@start $io @read @rest $($rest)*) }; (@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [$kind:tt; $len:expr] $($rest:tt)*) => { let $($mut)* $var = $io.scan_vec::<$kind>($len); input!(@start $io @read @rest $($rest)*) }; (@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: $kind:tt $($rest:tt)*) => { let $($mut)* $var = $io.scan::<$kind>(); input!(@start $io @read @rest $($rest)*) }; (from $io:tt $($rest:tt)*) => { input!(@start $io @read @rest $($rest)*) }; } } // ------------ io module end ------------