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;
#define REP(i,n) for(int i=0;i<int(n);i++)
typedef long long ll;

const int N = 4010;

int n,x;
int a[N],b[N][N];

int main() {
  scanf("%d%d",&n,&x);
  REP(i,n) scanf("%d", &a[i]), a[i+n] = a[i];

  REP(i,n) {
    b[i][i] = a[i];
    for(int j=i+1;j<n+n;j++) b[i][j] = min(b[i][j-1], a[j]);
  }
  ll ans = 9e18;
  REP(s,n) {
    ll cur = 1ll * s * x;
    REP(i,n) cur += b[i][s+i];
    ans = min(ans, cur);
  }
  printf("%lld\n", ans);

  return 0;
}
