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;
using lli = long long int;
using Vint = vector<int>;
using Vlli = vector<lli>;
using Wint = vector<Vint>;
using Wlli = vector<Vlli>;
using pii = pair<int, int>;
using pll = pair<lli, lli>;
const int MOD = 1e9 + 7;
const int INFi = 2e9 + 1;
const lli INFl = (lli)(9e18) + 1;
const vector<pii> DXDY = {make_pair(1, 0), make_pair(-1, 0), make_pair(0, 1),
                          make_pair(0, -1)};
const char BR = '\n';
template <class T>
inline int argmin(vector<T> vec) {
  return min_element(vec.begin(), vec.end()) - vec.begin();
}
template <class T>
inline int argmax(vector<T> vec) {
  return max_element(vec.begin(), vec.end()) - vec.begin();
}
template <class T>
inline void chmax(T &a, T b) {
  a = max(a, b);
}
template <class T>
inline void chmin(T &a, T b) {
  a = min(a, b);
}
inline int toInt(string &s) {
  int res = 0;
  for (char a : s) res = 10 * res + (a - '0');
  return res;
}
inline int toInt(const string s) {
  int res = 0;
  for (char a : s) res = 10 * res + (a - '0');
  return res;
}
inline long long int toLong(string &s) {
  lli res = 0;
  for (char a : s) res = 10 * res + (a - '0');
  return res;
}
inline long long int toLong(const string s) {
  lli res = 0;
  for (char a : s) res = 10 * res + (a - '0');
  return res;
}
template <class T>
inline std::string toString(T n) {
  if (n == 0) return "0";
  std::string res = "";
  if (n < 0) {
    n = -n;
    while (n != 0) {
      res += (char)(n % 10 + '0');
      n /= 10;
    }
    std::reverse(res.begin(), res.end());
    return '-' + res;
  }
  while (n != 0) {
    res += (char)(n % 10 + '0');
    n /= 10;
  }
  std::reverse(res.begin(), res.end());
  return res;
}
int main(void) {
  int n, x, min_A = INFi;
  scanf("%d%d", &n, &x);
  Vint A(n);
  for (auto &(ele) : (A)) {
    scanf("%d", &ele);
    chmin(min_A, ele);
  }
  lli res = 0;
  int CG = min_A + x;
  for (auto &(ele) : (A)) res += min(ele, CG);
  cout << res << BR;
  return 0;
}
