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;
int cost[2000];
bool own[2000];
int n;
unsigned long long x;
inline unsigned long long decide() {
  unsigned long long costtt = 2147483647;
  int minplace = 0;
  unsigned long long sum = 0, sumslide = 0;
  bool gotdemall = true;
  for (int i = 0; i < n; ++i) {
    if (!own[i]) {
      sum += cost[i];
      gotdemall = false;
      if (cost[i] < costtt) {
        minplace = i;
        costtt = cost[i];
      }
    }
    if (i) {
      if (!own[i - 1]) {
        sumslide += cost[i];
      }
    } else if (!own[n - 1]) {
      sumslide += cost[0];
    }
  }
  if (gotdemall) return 0;
  if (sumslide + x < sum) {
    int tmp = own[n - 1];
    for (int i = n; --i;) own[i] = own[i - 1];
    own[0] = tmp;
    costtt = x;
  } else
    own[minplace] = 1;
  return costtt + decide();
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> x;
  for (int i = 0; i < n; ++i) cin >> cost[i];
  cout << decide();
}
