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;

typedef long long ll;

ll C[2020], K[2020];
ll n,x,ans;

int main()
{
	ll i,j,k;
	
	ans = 1e18;
	
	scanf("%lld%lld",&n,&x);
	
	for(i=0;i<n;i++){
		scanf("%lld",C+i);
		K[i] = C[i];
	}
	
	for(i=0;i<n;i++){
		k = x * i;
		for(j=0;j<n;j++){
			K[j] = min(K[j], C[(j-i+n)%n]);
			k += K[j];
		}
		ans = min(ans, k);
	}
	
	printf("%lld\n",ans);
	
	return 0;
}