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 ll = long long;

ll A[2010];
ll T[2010];

int main(){
    ll N, x;
    cin >> N >> x;
    ll ans = 0;
    for(ll i=0; i<N; i++){
        cin >> A[i];
        T[i] = A[i];
        ans += T[i];
    }

    for(ll p=1; p<N; p++){
        ll sum = p * x;
        for(ll i=0; i<N; i++){
            T[i] = min(T[i], A[(i-p+N)%N]);
            sum += T[i];
        }
        ans = min(ans, sum);
    }
    cout << ans << endl; 
    return 0;
}
