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
N,x,a[2000],d[2000][2000],i,k;long long t,s;main(p,q){
	scanf("%d%d",&N,&x);
	for(;~scanf("%d",a+i);++i)s+=d[i][i]=a[i];
	for(;++k<N;s=t<s?t:s)
		for(t=k*x,i=0;i<N;++i)
			t+=d[(i-k+N)%N][i]=(p=a[(i-k+N)%N])<(q=d[(i-k+1+N)%N][i])?p:q;
	k=!printf("%lld\n",s);
}
