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
///
// File:  b.go
// Author: ymiyamoto
//
// Created on Sun May  6 12:41:16 2018
//
package main

import (
	"fmt"
)

var N, x int
var arr []int

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func main() {
	fmt.Scan(&N, &x)
	arr = make([]int, N)
	for i := range arr {
		fmt.Scan(&arr[i])
	}

	ans := 1 << 30
	for k := 0; k < N; k++ {
		catch := 0
		for i := 0; i < N; i++ {
			m := 1 << 30
			for j := i - k; j <= i; j++ {
				m = min(m, arr[(j+N)%N])
			}
			catch += m
		}
		ans = min(ans, x*k+catch)
	}

	fmt.Println(ans)
}
