Problem:
Score : 400 points

Problem Statement

Find the largest integer that can be formed with exactly N matchsticks, under the following conditions:

Every digit in the integer must be one of the digits A_1, A_2, ..., A_M (1 \leq A_i \leq 9).

The number of matchsticks used to form digits 1, 2, 3, 4, 5, 6, 7, 8, 9 should be 2, 5, 5, 4, 5, 6, 3, 7, 6, respectively.

Constraints

All values in input are integers.

2 \leq N \leq 10^4

1 \leq M \leq 9

1 \leq A_i \leq 9

A_i are all different.

There exists an integer that can be formed by exactly N matchsticks under the conditions.

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 ... A_M

Output

Print the largest integer that can be formed with exactly N matchsticks under the conditions in the problem statement.

Sample Input 1

20 4
3 7 8 4

Sample Output 1

777773

The integer 777773 can be formed with 3 + 3 + 3 + 3 + 3 + 5 = 20 matchsticks, and this is the largest integer that can be formed by 20 matchsticks under the conditions.

Sample Input 2

101 9
9 8 7 6 5 4 3 2 1

Sample Output 2

71111111111111111111111111111111111111111111111111

The output may not fit into a 64-bit integer type.

Sample Input 3

15 3
5 4 6

Sample Output 3

654

Solution in Rust (1.15.1) (judge verdict: Accepted)

pub trait FromFragments {
    #[doc = " Output type."]
    #[doc = ""]
    #[doc = " In almost all cases, `Output` should be `Self`."]
    #[doc = " This type field exists for implementing 1-origin to 0-origin conversion"]
    #[doc = " by `usize_` etc."]
    type Output;
    #[doc = " Returns how many words are read."]
    fn fragments_count() -> usize;
    #[doc = " Converts words into `Output`s."]
    #[doc = ""]
    #[doc = " If the conversion fails, returns `Err` with error message."]
    #[doc = ""]
    #[doc = " # Panics"]
    #[doc = ""]
    #[doc = " If `fragments.len()` differs from `fragments_count()`,"]
    #[doc = " the method may panic."]
    fn from_fragments(fragments: &[&str]) -> Result<Self::Output, String>;
}
#[macro_export]
macro_rules! readable {
    ( $ t : ty , |$ fragments : ident | $ from_fragments : expr ) => {
        readable!($t, 1, |$fragments| $from_fragments);
    };
    ( $ t : ty , $ fragments_count : expr , |$ fragments : ident | $ from_fragments : expr ) => {
        impl FromFragments for $t {
            type Output = $t;
            fn fragments_count() -> usize {
                $fragments_count
            }
            fn from_fragments($fragments: &[&str]) -> Result<$t, String> {
                Ok($from_fragments)
            }
        }
    };
}
readable!((), |_ss| ());
readable!(String, |ss| ss[0].to_string());
macro_rules ! impl_from_fragments { ( $ ( $ t : ty ) * ) => { $ ( impl FromFragments for $ t { type Output = Self ; fn fragments_count ( ) -> usize { 1 } fn from_fragments ( fragments : & [ & str ] ) -> Result <$ t , String > { use std :: str :: FromStr ; <$ t >:: from_str ( fragments [ 0 ] ) . map_err ( | _ | { format ! ( "cannot parse \"{}\" as {}" , fragments [ 0 ] , stringify ! ( $ t ) ) } ) } } ) * } ; }
impl_from_fragments ! ( i8 u8 i16 u16 i32 u32 i64 u64 isize usize f32 f64 ) ;
macro_rules ! define_one_origin_int_types { ( $ new_t : ident $ int_t : ty ) => { # [ doc = " Convert 1-origin integer into 0-origin when read from input." ] # [ allow ( non_camel_case_types ) ] pub struct $ new_t ( ) ; impl FromFragments for $ new_t { type Output = $ int_t ; fn fragments_count ( ) -> usize { 1 } fn from_fragments ( fragments : & [ & str ] ) -> Result < Self :: Output , String > { <$ int_t >:: from_fragments ( fragments ) . map ( | n | n - 1 ) } } } ; ( $ new_t : ident $ int_t : ty ; $ ( $ inner_new_t : ident $ inner_int_t : ty ) ;* ) => { define_one_origin_int_types ! ( $ new_t $ int_t ) ; define_one_origin_int_types ! ( $ ( $ inner_new_t $ inner_int_t ) ;* ) ; } ; }
define_one_origin_int_types ! ( u64_ u64 ; usize_ usize ) ;
macro_rules ! impl_from_fragments_for_tuples { ( $ t : ident $ var : ident $ count : expr ) => ( ) ; ( $ t : ident $ var : ident $ count : expr ; $ ( $ inner_t : ident $ inner_var : ident $ inner_count : expr ) ;* ) => { impl_from_fragments_for_tuples ! ( $ ( $ inner_t $ inner_var $ inner_count ) ;* ) ; impl <$ t : FromFragments , $ ( $ inner_t : FromFragments ) ,*> FromFragments for ( $ t , $ ( $ inner_t ) ,* ) { type Output = ( <$ t >:: Output , $ ( <$ inner_t >:: Output ) ,* ) ; fn fragments_count ( ) -> usize { let mut n = <$ t >:: fragments_count ( ) ; $ ( n += <$ inner_t >:: fragments_count ( ) ; ) * n } # [ allow ( unused_assignments ) ] fn from_fragments ( fragments : & [ & str ] ) -> Result < Self :: Output , String > { let mut start = 0 ; let $ var = <$ t >:: from_fragments ( & fragments [ start .. start +<$ t >:: fragments_count ( ) ] ) ?; start += <$ t >:: fragments_count ( ) ; $ ( let $ inner_var = <$ inner_t >:: from_fragments ( & fragments [ start .. start +<$ inner_t >:: fragments_count ( ) ] ) ?; start += <$ inner_t >:: fragments_count ( ) ; ) * Ok ( ( $ var , $ ( $ inner_var ) ,* ) ) } } } ; }
impl_from_fragments_for_tuples ! ( T4 x4 4 ; T3 x3 3 ; T2 x2 2 ; T1 x1 1 ) ;
pub trait FromLine: Sized {
    type Output;
    fn from_line(line: &str) -> Result<Self::Output, String>;
}
fn split_into_fragments(line: &str) -> Vec<&str> {
    #[allow(deprecated)]
    line.trim_right_matches('\n').split_whitespace().collect()
}
impl<T: FromFragments> FromLine for T {
    type Output = T::Output;
    fn from_line(line: &str) -> Result<T::Output, String> {
        let fragments = split_into_fragments(line);
        if fragments.len() != T::fragments_count() {
            return Err(format!(
                "line \"{}\" has {} fragments, expected {}",
                line,
                fragments.len(),
                T::fragments_count()
            ));
        }
        T::from_fragments(&fragments)
    }
}
impl<T: FromFragments> FromLine for Vec<T> {
    type Output = Vec<T::Output>;
    fn from_line(line: &str) -> Result<Self::Output, String> {
        let n = T::fragments_count();
        let fragments = split_into_fragments(line);
        if fragments.len() % n != 0 {
            return Err(format!(
                "line \"{}\" has {} fragments, expected multiple of {}",
                line,
                fragments.len(),
                n
            ));
        }
        let mut result = Vec::new();
        for chunk in fragments.chunks(n) {
            match T::from_fragments(chunk) {
                Ok(v) => result.push(v),
                Err(msg) => {
                    let flagment_msg = if n == 1 {
                        format!("fragment {}", result.len())
                    } else {
                        let l = result.len();
                        format!("fragments {}-{}", n * l + 1, (n + 1) * l)
                    };
                    return Err(format!("{} of line \"{}\": {}", flagment_msg, line, msg));
                }
            }
        }
        Ok(result)
    }
}
pub fn read<T: FromLine>() -> T::Output {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    T::from_line(&line).unwrap()
}
#[macro_export]
macro_rules ! read { ( ) => { let mut line = String :: new ( ) ; std :: io :: stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; } ; ( $ pat : pat = $ t : ty ) => { let $ pat = read ::<$ t > ( ) ; } ; ( $ ( $ pat : pat = $ t : ty ) ,+ ) => { read ! ( ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) ) ; } ; }
#[macro_export]
macro_rules ! readls { ( $ ( $ pat : pat = $ t : ty ) ,+ ) => { $ ( read ! ( $ pat = $ t ) ; ) * } ; }
pub fn readx<T: FromLine>() -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result = stdin
        .lock()
        .lines()
        .map(|line_result| {
            let line = line_result.expect("read from stdin failed");
            T::from_line(&line).unwrap()
        }).collect();
    result
}
#[macro_export]
macro_rules ! readx_loop { ( $ pat : pat = $ t : ty ; $ block : block ) => { use std :: io :: BufRead ; let stdin = std :: io :: stdin ( ) ; for line in stdin . lock ( ) . lines ( ) { let line = line . expect ( "read from stdin failed" ) ; let $ pat = <$ t >:: from_line ( & line ) . unwrap ( ) ; $ block } } ; ( $ ( $ pat : pat = $ t : ty ) ,* ; $ block : block ) => { readx_loop ! ( ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) ; $ block ) ; } ; }
#[macro_export]
macro_rules ! readn_loop { ( $ n : expr ; $ pat : pat = $ t : ty ; $ block : block ) => { use std :: io :: BufRead ; let stdin = std :: io :: stdin ( ) ; { let lock = stdin . lock ( ) ; for _ in 0 ..$ n { let line = String :: new ( ) ; lock . read_line ( & mut line ) . expect ( "read from stdin failed" ) ; let $ pat = <$ t >:: from_line ( & line ) . unwrap ( ) ; $ block } } } ; ( $ n : expr ; $ ( $ pat : pat = $ t : ty ) ,* ; $ block : block ) => { read_times_loop ! ( $ n ; ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) ; $ block ) ; } ; }
pub trait ReadExt {
    fn read<T: FromFragments>(&self) -> T::Output;
}
impl<'a> ReadExt for [&'a str] {
    fn read<T: FromFragments>(&self) -> T::Output {
        T::from_fragments(self).unwrap()
    }
}
impl<'a> ReadExt for &'a str {
    fn read<T: FromFragments>(&self) -> T::Output {
        T::from_fragments(&[self]).unwrap()
    }
}

#[macro_export]
macro_rules! dbg {
    ( $ e : expr ) => {{
        use std::io::{self, Write};
        let result = $e;
        writeln!(
            io::stderr(),
            "{}: {} = {:?}",
            line!(),
            stringify!($e),
            result
        ).unwrap();
        result
    }};
}

#[derive(Clone)]
pub struct StepBy<I> {
    iter: I,
    step: usize,
    first_take: bool,
}
impl<I: Iterator> Iterator for StepBy<I> {
    type Item = I::Item;
    fn next(&mut self) -> Option<Self::Item> {
        if self.first_take {
            self.first_take = false;
            self.iter.next()
        } else {
            self.iter.nth(self.step)
        }
    }
}
#[derive(Clone)]
pub struct LScan<I: Iterator, S: Clone, F: FnMut(&S, I::Item) -> S> {
    iter: I,
    state: Option<S>,
    f: F,
}
impl<I: Iterator, S: Clone, F> Iterator for LScan<I, S, F>
where
    F: FnMut(&S, I::Item) -> S,
{
    type Item = S;
    fn next(&mut self) -> Option<S> {
        if self.state.is_none() {
            return None;
        }
        let state_inner = self.state.take().unwrap();
        if let Some(item) = self.iter.next() {
            self.state = Some((self.f)(&state_inner, item));
        }
        Some(state_inner)
    }
}
pub struct Flatten<I: Iterator>
where
    I::Item: IntoIterator,
{
    outer_iter: I,
    inner_iter: Option<<<I as Iterator>::Item as IntoIterator>::IntoIter>,
}
impl<I, J> Iterator for Flatten<I>
where
    I: Iterator<Item = J>,
    J: IntoIterator,
{
    type Item = <<J as IntoIterator>::IntoIter as Iterator>::Item;
    fn next(&mut self) -> Option<J::Item> {
        loop {
            if let Some(inner_iter) = self.inner_iter.as_mut() {
                if let item @ Some(_) = inner_iter.next() {
                    return item;
                }
            }
            match self.outer_iter.next() {
                None => return None,
                Some(inner) => self.inner_iter = Some(inner.into_iter()),
            }
        }
    }
}
use std::fmt;
trait RichIterator: Iterator {
    fn step_by_(self, step: usize) -> StepBy<Self>
    where
        Self: Sized,
    {
        assert_ne!(step, 0);
        StepBy {
            iter: self,
            step: step - 1,
            first_take: true,
        }
    }
    fn for_each<F: FnMut(Self::Item)>(self, mut f: F)
    where
        Self: Sized,
    {
        for item in self {
            f(item);
        }
    }
    fn lscan<S: Clone, F>(self, state: S, f: F) -> LScan<Self, S, F>
    where
        Self: Sized,
        F: FnMut(&S, Self::Item) -> S,
    {
        LScan {
            iter: self,
            state: Some(state),
            f: f,
        }
    }
    fn get_unique(mut self) -> Option<Self::Item>
    where
        Self: Sized,
        Self::Item: Eq,
    {
        let first_opt = self.next();
        first_opt.and_then(|first| {
            if self.all(|item| item == first) {
                Some(first)
            } else {
                None
            }
        })
    }
    fn flatten(mut self) -> Flatten<Self>
    where
        Self: Sized,
        Self::Item: IntoIterator,
    {
        let inner_opt = self.next();
        Flatten {
            outer_iter: self,
            inner_iter: inner_opt.map(|inner| inner.into_iter()),
        }
    }
    fn join(mut self, sep: &str) -> String
    where
        Self: Sized,
        Self::Item: fmt::Display,
    {
        let mut result = String::new();
        if let Some(first) = self.next() {
            result.push_str(&format!("{}", first));
        }
        for s in self {
            result.push_str(&format!("{}{}", sep, s));
        }
        result
    }
    fn cat(self) -> String
    where
        Self: Sized,
        Self::Item: fmt::Display,
    {
        self.join("")
    }
}
impl<I: Iterator> RichIterator for I {}
pub struct Unfold<T, F>
where
    F: FnMut(&T) -> Option<T>,
{
    state: Option<T>,
    f: F,
}
impl<T, F> Iterator for Unfold<T, F>
where
    F: FnMut(&T) -> Option<T>,
{
    type Item = T;
    fn next(&mut self) -> Option<T> {
        if self.state.is_none() {
            return None;
        }
        let state_inner = self.state.take().unwrap();
        self.state = (self.f)(&state_inner);
        Some(state_inner)
    }
}
pub fn unfold<T, F>(init: T, f: F) -> Unfold<T, F>
where
    F: FnMut(&T) -> Option<T>,
{
    Unfold {
        state: Some(init),
        f: f,
    }
}
pub struct Iterate<T, F>
where
    F: FnMut(&T) -> T,
{
    state: T,
    f: F,
}
impl<T, F> Iterator for Iterate<T, F>
where
    F: FnMut(&T) -> T,
{
    type Item = T;
    fn next(&mut self) -> Option<T> {
        use std::mem::swap;
        let mut state = (self.f)(&self.state);
        swap(&mut state, &mut self.state);
        Some(state)
    }
}
pub fn iterate<T, F>(init: T, f: F) -> Iterate<T, F>
where
    F: FnMut(&T) -> T,
{
    Iterate { state: init, f: f }
}


fn flatten<T>(x: Option<Option<T>>) -> Option<T> {
    match x {
        Some(inner) => inner,
        _ => None
    }
}

use std::collections::HashMap;

fn search(
    nums: &[u8],
    rest: u16,
    most_efficient: (u16, u8),
    bigger: &[(u16, u8)],
    smaller: &[(u16, u8)]
) -> Option<Vec<u8>> {
    if rest == 0 {
        return Some(nums.to_vec())
    }

    nums.split_first().and_then(|(_, tail)| {
        flatten(bigger.iter().map(|&(nbars, num)| {
            rest.checked_sub(nbars - most_efficient.0).and_then(|next_rest| {
                search(tail, next_rest, most_efficient, bigger, smaller)
                    .map(|mut tail| {
                        tail.insert(0, num);
                        tail
                    })
            })
        }).find(|x| x.is_some()))
    }).or_else(|| {
        nums.split_last().and_then(|(_, first)| {
            flatten(smaller.iter().map(|&(nbars, num)| {
                rest.checked_sub(nbars - most_efficient.0).and_then(|next_rest| {
                    search(first, next_rest, most_efficient, bigger, smaller)
                        .map(|mut first| {
                            first.push(num);
                            first
                        })
                })
            }).find(|x| x.is_some()))
        })
    })
}

use std::cmp::{Ord, Ordering};
#[derive(Clone, Copy, PartialEq, Eq)]
struct Reverse<T>(T);
impl<T: PartialOrd> PartialOrd for Reverse<T> {
    fn partial_cmp(&self, other: &Reverse<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}
impl<T: Ord> Ord for Reverse<T> {
    fn cmp(&self, other: &Reverse<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}
trait SortDesc<T> {
    fn sort_desc(&mut self)
    where
        T: Ord;
    fn sort_desc_by_key<K: Ord, F: FnMut(&T) -> K>(&mut self, f: F);
}
impl<T> SortDesc<T> for [T] {
    fn sort_desc(&mut self)
    where
        T: Ord,
    {
        self.sort();
        self.reverse();
    }
    fn sort_desc_by_key<K: Ord, F: FnMut(&T) -> K>(&mut self, mut f: F) {
        self.sort_by_key(|x| Reverse(f(x)));
    }
}
#[derive(PartialEq, PartialOrd)]
struct Total<T: PartialOrd + PartialEq>(T);
impl<T: PartialOrd + PartialEq> Eq for Total<T> {}
impl<T: PartialOrd + PartialEq> Ord for Total<T> {
    fn cmp(&self, other: &Self) -> Ordering {
        self.partial_cmp(other).unwrap()
    }
}


fn main() {
    read!(n = u16, _ = ());
    read!(aa = Vec<u8>);
    let mut nbars_to_num = HashMap::new();
    let num_to_nbars = [0, 2, 5, 5, 4, 5, 6, 3, 7, 6];
    for a in aa {
        let num = nbars_to_num.entry(num_to_nbars[a as usize]).or_insert(0);
        if *num < a {
            *num = a;
        }
    }
    let mut nbars_and_num: Vec<(u16, u8)> = nbars_to_num.into_iter().collect();
    nbars_and_num.sort_by_key(|&(nbars, _num)| nbars);
    let most_efficient = nbars_and_num[0];

    let mut bigger: Vec<(u16, u8)> = nbars_and_num.iter()
        .filter(|&&(_nbars, num)| num > most_efficient.1)
        .map(|&x| x)
        .collect();
    bigger.sort_desc_by_key(|&(_nbars, num)| num);
    let mut smaller: Vec<(u16, u8)> = nbars_and_num.iter()
        .filter(|&&(_nbars, num)| num < most_efficient.1)
        .map(|&x| x)
        .collect();
    smaller.sort_by_key(|&(_nbars, num)| num);

    let ans = (0..n/most_efficient.0 + 1).rev()
        .map(|i| (vec![most_efficient.1; i as usize], n - i*most_efficient.0))
        .map(|(nums, rest)| search(&nums, rest, most_efficient, &bigger, &smaller))
        .find(|x| x.is_some())
        .unwrap()
        .unwrap();
    println!("{}", ans.into_iter().cat());
}