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 N, X;
int A[2000];
int B[2000];

int main()
{
    scanf("%d%d", &N, &X);
    for(int i=0; i<N; i++)
        scanf("%d", A+i), B[i]=A[i];
    long long ans=0x3f3f3f3f3f3f3f3fLL;
    for(int i=0; i<N; i++)
    {
        for(int j=0; j<N; j++)
            B[j]=min(B[j], A[(i+j)%N]);
        ans=min(ans, 1LL*i*X+accumulate(B, B+N, 0LL));
    }
    printf("%lld\n", ans);
    return 0;
}
