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<stdio.h>
int main(){
long n,i,j,a[2222],min[2222][2222],ans,x,p;
scanf("%ld%ld",&n,&x);
for(i=0;i<n;i++)
scanf("%ld",&a[i]);
for(i=0;i<n;i++)
for(j=0;j<n;j++)
min[i][j]=100000000000;
for(i=0;i<n;i++){
for(j=0;j<n;j++){
if(a[(i-j)%n]<min[i][(i-j+1)%n])
min[i][(i-j)%n]=a[(i-j)%n];
else
min[i][(i-j)%n]=min[i][(i-j+1)%n];
}
ans=10000000000000;
for(i=0;i<n;i++){
p=0;
for(j=0;j<n;j++)
p+=min[i][(i-j)%n];
p+=j*x;
if(p<ans)
ans=p;
}
printf("%ld\n",ans);
return 0;
}