Problem:
Score : 600 points

Problem Statement

We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.

Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.

It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.

You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.

Constraints

0 ≤ K ≤ 50 \times 10^{16}

Input

Input is given from Standard Input in the following format:

K

Output

Print a solution in the following format:

N
a_1 a_2 ... a_N

Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.

Sample Input 1

0

Sample Output 1

4
3 3 3 3

Sample Input 2

1

Sample Output 2

3
1 0 3

Sample Input 3

2

Sample Output 3

2
2 2

The operation will be performed twice: [2, 2] -> [0, 3] -> [1, 1].

Sample Input 4

3

Sample Output 4

7
27 0 0 0 0 0 0

Sample Input 5

1234567894848

Sample Output 5

10
1000 193 256 777 0 1 1192 1234567891011 48 425

Solution in Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports, unused_macros)]

use kyoproio::*;
use std::{
    collections::*,
    io::{self, prelude::*},
    iter,
    mem::{replace, swap},
};

fn main() -> io::Result<()> {
    std::thread::Builder::new()
        .stack_size(64 * 1024 * 1024)
        .spawn(|| {
            let stdin = io::stdin();
            let stdout = io::stdout();
            run(KInput::new(stdin.lock()), io::BufWriter::new(stdout.lock()))
        })?
        .join()
        .unwrap();
    Ok(())
}

fn run<I: Input, O: Write>(mut kin: I, mut out: O) {
    macro_rules! output { ($($args:expr),+) => { write!(&mut out, $($args),+).unwrap(); }; }
    macro_rules! outputln {
        ($($args:expr),+) => { output!($($args),+); outputln!(); };
        () => { output!("\n"); if cfg!(debug_assertions) { out.flush().unwrap(); } }
    }

    let k: i64 = kin.input();
    
    if k == 0 {
        outputln!("2\n0 0");
    } else if k == 1 {
        outputln!("2\n2 0");
    } else {
        let n = k.min(50);
        outputln!("{}", n);
        for i in 0..n {
            let x = if i < k % n { k / n + 1 } else { k / n };
            let a = n - 1 - k + (n + 1) * x;
            output!("{} ", a);
        }
        outputln!();
    }
}


// -----------------------------------------------------------------------------
pub mod kyoproio {
    use std::io::prelude::*;
    pub trait Input {
        fn str(&mut self) -> &str;
        fn input<T: InputParse>(&mut self) -> T {
            T::input(self)
        }
        fn iter<T: InputParse>(&mut self) -> Iter<T, Self> {
            Iter(self, std::marker::PhantomData)
        }
        fn seq<T: InputParse, B: std::iter::FromIterator<T>>(&mut self, n: usize) -> B {
            self.iter().take(n).collect()
        }
    }
    pub struct KInput<R> {
        src: R,
        buf: String,
        pos: usize,
    }
    impl<R: BufRead> KInput<R> {
        pub fn new(src: R) -> Self {
            Self {
                src,
                buf: String::with_capacity(1024),
                pos: 0,
            }
        }
    }
    impl<R: BufRead> Input for KInput<R> {
        fn str(&mut self) -> &str {
            loop {
                if self.pos >= self.buf.len() {
                    self.pos = 0;
                    self.buf.clear();
                    if self.src.read_line(&mut self.buf).expect("io error") == 0 {
                        return &self.buf;
                    }
                }
                let range = self.pos
                    ..self.buf[self.pos..]
                        .find(|c: char| c.is_ascii_whitespace())
                        .map(|i| i + self.pos)
                        .unwrap_or_else(|| self.buf.len());
                self.pos = range.end + 1;
                if range.end > range.start {
                    return &self.buf[range];
                }
            }
        }
    }
    pub struct Iter<'a, T, I: ?Sized>(&'a mut I, std::marker::PhantomData<*const T>);
    impl<'a, T: InputParse, I: Input + ?Sized> Iterator for Iter<'a, T, I> {
        type Item = T;
        fn next(&mut self) -> Option<T> {
            Some(self.0.input())
        }
    }
    pub trait InputParse: Sized {
        fn input<I: Input + ?Sized>(src: &mut I) -> Self;
    }
    impl InputParse for Vec<u8> {
        fn input<I: Input + ?Sized>(src: &mut I) -> Self {
            src.str().as_bytes().to_owned()
        }
    }
    macro_rules! from_str_impl {
        { $($T:ty)* } => {
            $(impl InputParse for $T {
                fn input<I: Input + ?Sized>(src: &mut I) -> Self {
                    src.str().parse::<$T>().expect("parse error")
                }
            })*
        }
    }
    from_str_impl! {
        String char bool f32 f64 isize i8 i16 i32 i64 i128 usize u8 u16 u32 u64 u128
    }
    macro_rules! tuple_impl {
        ($H:ident $($T:ident)*) => {
            impl<$H: InputParse, $($T: InputParse),*> InputParse for ($H, $($T),*) {
                fn input<I: Input + ?Sized>(src: &mut I) -> Self {
                    ($H::input(src), $($T::input(src)),*)
                }
            }
            tuple_impl!($($T)*);
        };
        () => {}
    }
    tuple_impl!(A B C D E F G);
    #[macro_export]
    macro_rules! kdbg {
        ($($v:expr),*) => {
            if cfg!(debug_assertions) { dbg!($($v),*) } else { ($($v),*) }
        }
    }
}