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.

Examples

Input

2 10
1 100


Output

12


Input

3 10
100 1 100


Output

23


Input

4 10
1 2 3 4


Output

10
#![allow(unused)]

use proconio::*;
use std::cmp;

fn main() {
    input! {
        n: usize,
        x: u32,
        mut a: [u32; n],
    }

    let mut ans: u32 = a.iter().sum();
    for i in 1..=n {
        let mut b = a.clone();
        for j in 0..n {
            b[j] = cmp::min(a[(j + n - 1) % n], b[j])
        }
        a = b;

        ans = cmp::min(ans, a.iter().sum::<u32>() + x * i as u32);
    }
    println!("{}", ans);
}
