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 Feb 25 23:06:21 2018
//
package main

import (
	"fmt"
	"sort"
)

func main() {
	var N int
	fmt.Scan(&N)

	arr := make([]int, N)
	acc := make([]int, N)
	for i := 0; i < N; i++ {
		var A int
		fmt.Scan(&A)
		arr[i] = A
		acc[i] = A
	}
	sort.Ints(arr)
	sort.Ints(acc)

	for i := 1; i < N; i++ {
		acc[i] += acc[i-1]
	}

	count := -1
	for i := 0; i < N; i++ {
		if i+1 < N && 2*acc[i] < arr[i+1] {
			count = i
		}
	}

	fmt.Println(N - (count + 1))
}
