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 <iostream>
# include <cmath>
# include <algorithm>
# include <stdio.h>
# include <cstdint>
# include <cstring>
# include <string>
# include <cstdlib>
# include <vector>
# include <bitset>
# include <map>
# include <queue>
# include <ctime>
# include <stack>
# include <set>
# include <list>
# include <random>
# include <deque>
# include <functional>
# include <iomanip>
# include <sstream>
# include <fstream>
# include <complex>
# include <numeric>
# include <immintrin.h>
# include <cassert>
# include <array>
# include <tuple>
# include <unordered_map>
# include <unordered_set>
# include <thread>

using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using ui32 = unsigned int;
constexpr ll INFLL = 1e18;

#define CHECK_IMPL1(cond)              \
if (!(cond)) {                         \
    DEBUG("expected cond: " << #cond); \
    assert(cond);                      \
}

#define CHECK_IMPL2(cond, message)                                            \
if (!(cond)) {                                                                \
    DEBUG("expected cond: " << #cond << " failed with message: " << message); \
    assert(cond);                                                             \
}
#define CHECK_IMPL(_1, _2, NAME, ...) NAME
#define CHECK(...) CHECK_IMPL(__VA_ARGS__, CHECK_IMPL2, CHECK_IMPL1, CHECK_IMPL0)(__VA_ARGS__)

#ifdef __APPLE__
#define DEBUG(message) std::cerr << message << std::endl;
#else
#define DEBUG(message)
#endif

void solve() {
  int n, x;
  cin >> n >> x;
  vector<int> a(n);
  vector<int> dp(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    dp[i] = a[i];
  }
  ll ans = INFLL;
  for (int k = 0; k <= 2 * n; k++) {
    ll cur = 0;
    for (int i = 0; i < n; i++) {
      int p = i - k;
      while (p < 0) {
        p += n;
      }
      dp[i] = min(dp[i], a[p]);
      cur += dp[i];
    }
    ans = min(ans, cur + 1LL * k * x);
  }
  cout << ans << "\n";
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
#ifdef __APPLE__
  freopen("input.txt", "r", stdin);
  // freopen("output.txt", "w", stdout);
#endif
  int t = 1;
  for (int i = 1; i <= t; i++) {
    solve();
  }
  return 0;
}