You are given an array a consisting of n integers. Beauty of array is the maximum sum of some consecutive subarray of this array (this subarray may be empty). For example, the beauty of the array [10, -5, 10, -4, 1] is 15, and the beauty of the array [-3, -5, -1] is 0.

You may choose at most one consecutive subarray of a and multiply all values contained in this subarray by x. You want to maximize the beauty of array after applying at most one such operation.

Input

The first line contains two integers n and x (1 ≤ n ≤ 3 ⋅ 10^5, -100 ≤ x ≤ 100) — the length of array a and the integer x respectively.

The second line contains n integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the array a.

Output

Print one integer — the maximum possible beauty of array a after multiplying all values belonging to some consecutive subarray x.

Examples

Input


5 -2
-3 8 -2 1 -6


Output


22


Input


12 -3
1 3 3 7 1 3 3 7 1 3 3 7


Output


42


Input


5 10
-1 -2 -3 -4 -5


Output


0

Note

In the first test case we need to multiply the subarray [-2, 1, -6], and the array becomes [-3, 8, 4, -2, 12] with beauty 22 ([-3, 8, 4, -2, 12]).

In the second test case we don't need to multiply any subarray at all.

In the third test case no matter which subarray we multiply, the beauty of array will be equal to 0.
import java.util.*;


import java.io.*;
public class newclass {
	static class pair implements Comparable<pair>{
		int a;int b; 
		public pair(int a, int b) {
			this.a=a;
			this.b=b;
			
		}
        public int compareTo(pair p){
        	return(a-p.a==0)?b-p.b:a-p.a;
        }
        public String toString () {
        	return a+" "+b;
        }
	}
	  static long gcd(long a, long b) 
	    { 
	    if (a == 0) 
	        return b;  
	    return gcd(b % a, a);  
	    } 
	  static long lcm(int a, int b) 
	    { 
	        return 1l*(a*b)/gcd(a, b); 
	    } 
	
  public static void main(String[] args) throws IOException {
	  
	  Scanner sc = new Scanner(System.in);
	  PrintWriter out = new PrintWriter(System.out);
	   n = sc.nextInt();
	   x = sc.nextInt();
	   arr = new long[n];
	  for(int i=0; i<n; i++) arr[i] = sc.nextLong();
	  dp = new long[n+5][3];
	  for(long[]x:dp) Arrays.fill(x, -1);
	  long finall = 0;
	  for(int i=0; i<n; i++) finall = Math.max(finall, solve(i,0));
	  out.println(finall);
	  out.flush();
  }
  static int n;
  static long x;
  static long[] arr;
  static long[][]dp;
  static long solve(int i, int f) {
	  if(i>=n) return 0;
	  if(dp[i][f]!=-1) return dp[i][f];
	  long no =0;
	  long start =0;
	  long take =0;
	  long leave =0;
	  if(f==0) { start = x*arr[i]+ solve(i+1,1);
	     leave =arr[i]+ solve(i+1,0);}
	  else if(f==1) {
		   take = x*arr[i]+solve(i+1,1);
		   leave =arr[i]+ solve(i+1,2);
	  }
	  else if(f ==2) {
		  leave = arr[i]+solve(i+1,2);
	  }
	  return dp[i][f] = Math.max(Math.max(take,leave), Math.max(start, no));
  }
   static long pow(int a, int b) {
	   long ans =1;
	   while(b-->0) ans*=1l*a;
	   return ans;
   }
 static class Scanner 
  {
  	StringTokenizer st;
  	BufferedReader br;
 
  	public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}
 
  	public String next() throws IOException 
  	{
  		while (st == null || !st.hasMoreTokens()) 
  			st = new StringTokenizer(br.readLine());
  		return st.nextToken();
  	}
    public boolean check() throws IOException{ return st.hasMoreTokens();}
  	public int nextInt() throws IOException {return Integer.parseInt(next());}
  	
  	public long nextLong() throws IOException {return Long.parseLong(next());}
 
  	public String nextLine() throws IOException {return br.readLine();}
  	
  	public double nextDouble() throws IOException
  	{
  		String x = next();
  		StringBuilder sb = new StringBuilder("0");
  		double res = 0, f = 1;
  		boolean dec = false, neg = false;
  		int start = 0;
  		if(x.charAt(0) == '-')
  		{
  			neg = true;
  			start++;
  		}
  		for(int i = start; i < x.length(); i++)
  			if(x.charAt(i) == '.')
  			{
  				res = Long.parseLong(sb.toString());
  				sb = new StringBuilder("0");
  				dec = true;
  			}
  			else
  			{
  				sb.append(x.charAt(i));
  				if(dec)
  					f *= 10;
  			}
  		res += Long.parseLong(sb.toString()) / f;
  		return res * (neg?-1:1);
  	}
  	
  	public boolean ready() throws IOException {return br.ready();}
 
 
  }
 static void shuffle(int[] a)
	{
		int n = a.length;
		for(int i = 0; i < n; i++)
		{
			int r = i + (int)(Math.random() * (n - i));
			int tmp = a[i];
			a[i] = a[r];
			a[r] = tmp;
		}
	}
}