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
#include <bits/stdc++.h>
using namespace std;
long long N;
long long X;
vector<long long> A;
map<vector<bool>, long long> memo;
int dist(int from, int to) {
  if (to < from) to += N;
  return to - from;
}
int next(int x) { return (x + 1) % N; }
long long sum(vector<long long> &v) {
  long long ans = 0;
  for (auto x : v) ans += x;
  return ans;
}
bool allcap(vector<bool> &cap) {
  for (auto x : cap) {
    if (!x) return false;
  }
  return true;
}
long long texpect(vector<bool> &cap) {
  if (memo.count(cap)) {
    return memo[cap];
  }
  vector<bool> ccap = cap;
  long long ans = 0;
  while (!allcap(ccap)) {
    vector<bool> ccc(N);
    for (int i = 0; i < N; ++i) {
      ccc[next(i)] = ccap[i];
    }
    ccap = ccc;
    ans += X;
    for (int i = 0; i < N; ++i) {
      if (cap[i] && !ccap[i]) {
        ccap[i] = true;
        ans += A[i];
      }
    }
  }
  memo.insert(map<vector<bool>, long long>::value_type(cap, ans));
  return ans;
}
int main() {
  cin >> N >> X;
  vector<bool> cap(N);
  for (int i = 0; i < N; ++i) {
    long long z;
    cin >> z;
    A.push_back(z);
    cap[i] = false;
  }
  int i0 = min_element(A.begin(), A.end()) - A.begin();
  long long ans = A[i0];
  cap[i0] = true;
  while (!allcap(cap)) {
    long long tspell = texpect(cap);
    int mi = -1;
    int mm = INT_MAX;
    for (int i = 0; i < N; ++i) {
      if (!cap[i] && A[i] < mm) {
        mm = A[i];
        mi = i;
      }
    }
    vector<bool> ccap = cap;
    ccap[mi] = true;
    long long tcap = texpect(ccap) + A[mi];
    if (tspell <= tcap) {
      ans += tspell;
      break;
    } else {
      ans += A[mi];
      cap[mi] = true;
    }
  }
  cout << ans << endl;
  return 0;
}
