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: Wrong Answer)

/*{{{*/
#include <vector>
#include <list>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <unordered_map>
#include <unordered_set>
#include <cassert>
using namespace std;
typedef pair<int, int> PP;
typedef long long LL;
#define pb push_back
#define fr first
#define sc second
#define bitcnt __builtin_popcount
#define all(x) x.begin(), x.end()
inline int ri() {int x; scanf("%d", &x); return x;}
#define rep2(i, n, ...) for (int i = 0; i < (n); i ++) 
#define rep3(i, a, b, ...) for (int i = (a); i < (b); i ++)
#define GET_MACRO(_1, _2, _3, NAME, ...) NAME
#define rep(...) GET_MACRO(__VA_ARGS__, rep3, rep2)(__VA_ARGS__)
#define drep2(i, n, ...) for (int i = (n) - 1; i >= 0; i --)
#define drep3(i, a, b) for (int i = (a) - 1; i >= (b); i --)
#define drep(...) GET_MACRO(__VA_ARGS__, drep3, drep2)(__VA_ARGS__)
template<typename T>inline bool smax(T&a, T b){if(a<b){a=b;return true;}return false;} 
template<typename T>inline bool smin(T&a, T b){if(a>b){a=b;return true;}return false;} 
/*}}}*/


LL a[3000], n, m, b[3000];
int main() {
  #ifdef _TEST_
  freopen("input.txt", "r", stdin);
  //freopen("out.txt", "w", stdout);
  #endif
  cin >> n >> m;
  rep(i, n) cin >> a[i], b[i] = a[i];
  LL res = 0;
  rep(i, n) res += a[i];
  rep(i, n) {
    rep(j, n) smin(b[j], b[(j - i - 1 + n) % n]);
    LL s = 0;
    rep(j, n) s += b[j];
    smin(res, s + (i + 1) * m);
  }
  cout << res << endl;
  return 0;
}