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 modinv(long long a) {
  long long b = ((int)1e6 + 3), u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= ((int)1e6 + 3);
  if (u < 0) u += ((int)1e6 + 3);
  return u;
}
int exp(int a, int b) {
  long long res = 1;
  long long sum = a;
  for (int i = 0; i < 30; ++i) {
    if ((1 << (i)) & b) {
      res = (res * sum) % ((int)1e6 + 3);
    }
    sum = (sum * sum) % ((int)1e6 + 3);
  }
  return res;
}
vector<long long> input(int N) {
  vector<long long> line(N);
  for (int i = 0; i < (N); ++i) {
    cin >> line[i];
  }
  vector<long long> res(min_element((line).begin(), (line).end()), line.end());
  res.insert(res.end(), line.begin(),
             min_element((line).begin(), (line).end()));
  return res;
}
long long N, x;
vector<vector<long long> > dp;
vector<long long> line;
long long func(int place, int use) {
  if (place == N) return 0;
  if (dp[place][use] >= 0) return dp[place][use];
  long long res = func(place + 1, use) + line[use] + x;
  res = min(res, line[place] + func(place + 1, place));
  dp[place][use] = res;
  return res;
}
int main() {
  cin >> N >> x;
  line = input(N);
  dp.resize(N, vector<long long>(N, -1));
  cout << func(0, 0) << endl;
  return 0;
}
