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)

/*
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,avx,avx2")
#pragma GCC optimize("Os")
#pragma GCC target("avx2,fma")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("Os")
*/
#include <bits/stdc++.h>

typedef long long ll;
typedef long double ld; 

#define X first
#define Y second
#define MP make_pair

using namespace std;
    
const int N = 2e3 + 123;
const ll mod = 1e9 + 7;
const ll INF = 1e18;

int n;
ll a[N], x, dp[N][N];
ll res;

int main () {
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	
	cin >> n >> x;
	for(int i = 1;i <= n;i++){
		cin >> a[i];
		dp[0][i] = a[i];
		res += a[i];
	}

	for(int k = 1;k < n;k++){
		ll now = 0;
		for(int i = 1;i <= n;i++){
			int nxt = i - k;
			if(nxt <= 0)
				nxt += n;
			//cout << nxt << " " << i << "\n";
			dp[k][i] = min(dp[k - 1][i], a[nxt]);
			now += dp[k][i];
		}
		now += k * x;
		res = min(res, now);
	}

	cout << res;

	return 0;
}