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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const int INF = 1e9;
const ll LINF = 1e18;

/*
<url:https://agc004.contest.atcoder.jp/tasks/agc004_b>
問題文============================================================
 高橋君は異世界に住んでいます。 この世界には N 色のスライムがいます。
 最初、高橋君はどの色のスライムも飼っていません。 高橋君の目標は、全色のスライムを一緒に飼うことです。
 
 高橋君は次の 2 種類の操作を行えます。
 
 今飼っていないスライムの色 i (1≤i≤N) をひとつ選ぶ。 色 i のスライムを捕まえて飼う。この操作には ai 秒掛かる。
 
 魔法を唱える。 すると、今飼っている各スライムについて、色 i (1≤i≤N−1) のスライムは色 i+1 へ変色する。
 ただし、色 N のスライムは色 1 へ変色する。 この操作には x 秒掛かる。
 
 高橋君が全色のスライムを一緒に飼うためには、最短で合計何秒掛かるかを求めてください。
=================================================================

解説=============================================================

================================================================
*/
int main(void) {
	cin.tie(0); ios::sync_with_stdio(false);
    ll N,x; cin >> N >> x;
    vector<ll> a(N);
    for(auto &in:a) cin >> in;
    vector<ll> b(N,LINF);
    ll ans = LINF;
    // i * x + Σb[j]_i
    for(int i = 0; i < N;i++){
        ll tmp = 0;
        for(int j = 0; j < N;j++){
            b[j] = min(b[j],a[(j-i+N)%N]);
            tmp += b[j];
        }
        ans = min(ans,i*x+tmp);
    }
    cout << ans << endl;
	return 0;
}