use std::collections::*;
use std::io::Write;
type Map<K, V> = BTreeMap<K, V>;
type Set<T> = BTreeSet<T>;
type Deque<T> = VecDeque<T>;
fn main() {
input! {
n: usize,
m: usize,
a: [[usize; 6]; n],
}
const P: usize = 10;
let mut cnt = vec![0u8; 1 << P];
for a in a {
let mut bit = 0;
for a in a {
bit |= 1 << a;
}
for (i, c) in cnt.iter_mut().enumerate() {
if i & bit > 0 {
*c += 1;
}
}
}
let min = *cnt[1..].iter().min().unwrap();
let mut ans: Vec<Vec<u8>> = vec![];
let mut dp: Vec<[u8; 10]> = vec![];
for c in (min + 1).. {
for (i, cnt) in cnt.iter().enumerate().skip(1) {
if *cnt + 1 != c {
continue;
}
let k = i.count_ones();
let v = (0..P).filter(|p| i >> *p & 1 == 1).collect::<Vec<_>>();
let mut a = vec![0; c as usize];
a.extend((1..k).map(|_| 1));
while {
let mut state = [0; 10];
let mut s = 0;
let mut x = 0;
for a in a.iter() {
if *a == 0 {
s += 1;
} else {
state[v[x]] = s;
s = 0;
x += 1;
}
}
state[v[x]] = s;
dp.push(state);
a.next_permutation()
} {}
}
dp.sort();
dp.dedup();
use std::cmp::*;
let mut h = std::collections::BinaryHeap::new();
for state in dp.iter() {
let mut a = Vec::with_capacity(c as usize);
for (i, &s) in state.iter().enumerate() {
a.extend((0..s).map(|_| i as u8));
}
if let Some(x) = a.iter().position(|a| *a > 0) {
a[..=x].rotate_right(1);
h.push(Reverse(a));
}
}
while let Some(Reverse(mut a)) = h.pop() {
ans.push(a.clone());
if ans.len() == m {
break;
}
if a.next_permutation() {
h.push(Reverse(a));
}
}
if ans.len() == m {
break;
}
let mut next = vec![];
for state in dp {
for i in 0..10 {
let mut s = state;
s[i] += 1;
next.push(s);
}
}
dp = next;
}
ans.truncate(m);
use util::*;
println!("{}", ans.iter().map(|a| a.iter().join("")).join(" "));
}
// ---------- 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, $t)).collect::<Vec<_>>()
};
($iter:expr, chars) => {
read_value!($iter, String).chars().collect::<Vec<char>>()
};
($iter:expr, bytes) => {
read_value!($iter, String).bytes().collect::<Vec<u8>>()
};
($iter:expr, usize1) => {
read_value!($iter, usize) - 1
};
($iter:expr, $t:ty) => {
$iter.next().unwrap().parse::<$t>().expect("Parse error")
};
}
// ---------- end input macro ----------
// ---------- begin super slice ----------
pub trait SuperSlice {
type Item;
fn lower_bound(&self, key: &Self::Item) -> usize
where
Self::Item: Ord;
fn lower_bound_by<F>(&self, f: F) -> usize
where
F: FnMut(&Self::Item) -> std::cmp::Ordering;
fn lower_bound_by_key<K, F>(&self, key: &K, f: F) -> usize
where
K: Ord,
F: FnMut(&Self::Item) -> K;
fn upper_bound(&self, key: &Self::Item) -> usize
where
Self::Item: Ord;
fn upper_bound_by<F>(&self, f: F) -> usize
where
F: FnMut(&Self::Item) -> std::cmp::Ordering;
fn upper_bound_by_key<K, F>(&self, key: &K, f: F) -> usize
where
K: Ord,
F: FnMut(&Self::Item) -> K;
fn next_permutation(&mut self) -> bool
where
Self::Item: Ord;
fn next_permutation_by<F>(&mut self, f: F) -> bool
where
F: FnMut(&Self::Item, &Self::Item) -> std::cmp::Ordering;
fn prev_permutation(&mut self) -> bool
where
Self::Item: Ord;
}
impl<T> SuperSlice for [T] {
type Item = T;
fn lower_bound(&self, key: &Self::Item) -> usize
where
T: Ord,
{
self.lower_bound_by(|p| p.cmp(key))
}
fn lower_bound_by<F>(&self, mut f: F) -> usize
where
F: FnMut(&Self::Item) -> std::cmp::Ordering,
{
self.binary_search_by(|p| f(p).then(std::cmp::Ordering::Greater))
.unwrap_err()
}
fn lower_bound_by_key<K, F>(&self, key: &K, mut f: F) -> usize
where
K: Ord,
F: FnMut(&Self::Item) -> K,
{
self.lower_bound_by(|p| f(p).cmp(key))
}
fn upper_bound(&self, key: &Self::Item) -> usize
where
T: Ord,
{
self.upper_bound_by(|p| p.cmp(key))
}
fn upper_bound_by<F>(&self, mut f: F) -> usize
where
F: FnMut(&Self::Item) -> std::cmp::Ordering,
{
self.binary_search_by(|p| f(p).then(std::cmp::Ordering::Less))
.unwrap_err()
}
fn upper_bound_by_key<K, F>(&self, key: &K, mut f: F) -> usize
where
K: Ord,
F: FnMut(&Self::Item) -> K,
{
self.upper_bound_by(|p| f(p).cmp(key))
}
fn next_permutation(&mut self) -> bool
where
T: Ord,
{
self.next_permutation_by(|a, b| a.cmp(b))
}
fn next_permutation_by<F>(&mut self, mut f: F) -> bool
where
F: FnMut(&Self::Item, &Self::Item) -> std::cmp::Ordering,
{
use std::cmp::Ordering::*;
if let Some(x) = self.windows(2).rposition(|a| f(&a[0], &a[1]) == Less) {
let y = self.iter().rposition(|b| f(&self[x], b) == Less).unwrap();
self.swap(x, y);
self[(x + 1)..].reverse();
true
} else {
self.reverse();
false
}
}
fn prev_permutation(&mut self) -> bool
where
T: Ord,
{
self.next_permutation_by(|a, b| a.cmp(b).reverse())
}
}
// ---------- end super slice ----------
mod util {
pub trait Join {
fn join(self, sep: &str) -> String;
}
impl<T, I> Join for I
where
I: Iterator<Item = T>,
T: std::fmt::Display,
{
fn join(self, sep: &str) -> String {
let mut s = String::new();
use std::fmt::*;
for (i, v) in self.enumerate() {
if i > 0 {
write!(&mut s, "{}", sep).ok();
}
write!(&mut s, "{}", v).ok();
}
s
}
}
}