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>

const int N = 2010;
typedef long long ll;

int min[N], a[N];

int main(){
	int n, x;
	scanf("%d%d", &n, &x);
	for (int i = 0; i < n; ++ i){
		scanf("%d", &a[i]);
		min[i] = a[i];
	}
	ll ans = LLONG_MAX;
	for (int i = 0; i < n; ++ i){
		ll sum = 1ll * i * x;
		for (int j = 0; j < n; ++ j){
			sum += min[j];
		}
		ans = std::min(sum, ans);
		for (int j = 0; j < n; ++ j){
			min[j] = std::min(min[j], a[(j - i - 1 + n) % n]);
		}
	}
	printf("%lld\n", ans);
}