Problem:
Score : 400 points

Problem Statement

Snuke lives in another world, where slimes are real creatures and kept by some people.
Slimes come in N colors. Those colors are conveniently numbered 1 through N.
Snuke currently has no slime. His objective is to have slimes of all the colors together.

Snuke can perform the following two actions:

Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.

Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.

Find the minimum time that Snuke needs to have slimes in all N colors.

Constraints

2≤N≤2,000

a_i are integers.

1≤a_i≤10^9

x is an integer.

1≤x≤10^9

Input

The input is given from Standard Input in the following format:

N x
a_1 a_2 ... a_N

Output

Find the minimum time that Snuke needs to have slimes in all N colors.

Sample Input 1

2 10
1 100

Sample Output 1

12

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Cast the spell. The color of the slime changes: 1 → 2. This takes 10 seconds.

Catch a slime in color 1. This takes 1 second.

Sample Input 2

3 10
100 1 100

Sample Output 2

23

Snuke can act as follows:

Catch a slime in color 2. This takes 1 second.

Cast the spell. The color of the slime changes: 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Cast the soell. The color of each slime changes: 3 → 1, 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Sample Input 3

4 10
1 2 3 4

Sample Output 3

10

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Catch a slime in color 2. This takes 2 seconds.

Catch a slime in color 3. This takes 3 seconds.

Catch a slime in color 4. This takes 4 seconds.

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

use std::collections::BinaryHeap;
use std::cmp;

fn main(){
    let mut sc = Scanner::new();
    let n = sc.next();
    let x : i64 = sc.next();
    let mut a = vec![0i64; n];
    for e in a.iter_mut() { *e = sc.next(); }
    let mut ans = a.iter().fold(0, |x, y| x + y);
    a.resize(n*2, 0);
    for i in 0..n { a[i+n] = a[i]; }

    let mut del = vec![false; n*2];
    let mut s:BinaryHeap<(i64, usize)> = BinaryHeap::new();
    for mg in 1..n {
        s.clear();
        s = (n-mg..n).map(|i| (-a[i], i)).collect();
        for i in 0..n*2 { del[i] = false; }
        let mut cand = x*mg as i64;
        for j in n..n+n {
            while del[s.peek().unwrap().1] {
                s.pop();
            }
            let min = *s.peek().unwrap();
            cand += cmp::min(-min.0 as i64, a[j]);
            del[j-mg] = true;
            s.push((-a[j], j));
        }
        ans = cmp::min(ans, cand);
    }
    println!("{}", ans);
}

// Scanner

#[allow(dead_code)]
struct Scanner {
    token_buffer : Vec<String>,
    index : usize,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner{
        Scanner { token_buffer: vec![], index: 0 }
    }

    fn wrapped<T>(& mut self) -> Result<T,&str> where T: std::str::FromStr {
        let s = try!(self.fetch_token());
        let t = try!(s.parse::<T>().map_err(|_| "Parse error"));
        Ok(t)
    }
    fn next<T>(& mut self) -> T where T: std::str::FromStr {
        self.wrapped::<T>().unwrap()
    }

    fn fetch_token(&mut self) -> Result<&String,&str> {
        while self.index >= self.token_buffer.len() {
            let mut st = String::new();
            while st.trim() == "" {
                match std::io::stdin().read_line(&mut st) {
                    Ok(l) if l > 0 => continue,
                    Ok(_)  => return Err("End of file"),
                    Err(_) => return Err("Failed to read line"),
                }
            }
            self.token_buffer = st.split_whitespace()
                .map(|x| x.to_string())
                .collect();
            self.index = 0;
        }

        self.index += 1;
        Ok(&self.token_buffer[self.index - 1])
    }
}