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 int long long
const int N = 2e3+5;
int dp[N][N], A[N], n, x, rt;
int32_t main(){
    scanf("%lld %lld", &n, &x);
    for(int i=0;i<n;i++) { scanf("%lld", &A[i]); dp[i][0] = A[i]; rt+=A[i]; }
    for(int i=1;i<n;i++){
        for(int j=0;j<n;j++) dp[j][i] = min(dp[j][i-1], A[(j-i+n)%n]);
        int sm = i*x;
        for(int j=0;j<n;j++) sm+=dp[j][i];
        rt = min(rt, sm);
    }
    printf("%lld", rt);
}