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
// Author : SAGORIKA DAS
#include <bits/stdc++.h>
using namespace std;
#define F first
#define S second
#define mp make_pair
#define pb push_back
#define CLEAR(a) memset(a,0,sizeof a)
#define REP(i,n) for(int i=0;i<n;i++)
#define FOR(i,a,b) for(int i=a;i<=b;i++)
#define fr freopen("input.txt", "r", stdin);
#define fw freopen("output.txt", "w", stdout);
#define int long long 
typedef long long LL;
typedef pair<int,int> pii;
const int MOD = 1e9 + 7;
const int MAX = 1e5 + 5;
int a[MAX];

 main() {
    //fr;fw;
    int n, x;
    cin >> n >> x;
    REP(i,n) cin >> a[i];
    int ret = 0;
    int mn = min_element(a,a +n)-a;
    for(int i=0;i<n;i++){
      if(a[i] > x+a[mn]) ret += x+a[mn];
      else ret += a[i];
    }
    cout << ret;
    return 0;
}