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.io.*;
import java.util.*;
import java.text.*;
import java.lang.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.regex.*;
import java.util.stream.LongStream;

public class Main{

	static ArrayList a[]=new ArrayList[200001];
	
	public static void main(String[] args)
   {
       InputReader in=new InputReader(System.in);
       PrintWriter pw = new PrintWriter(System.out);
       int n=in.nextInt();
       long d=in.nextLong();
       long a[]=new long[n];
       for(int i=0;i<n;i++)
    	   a[i]=in.nextLong();
       long pre[]=new long[n+1];
       long suf[]=new long[n+1];
       long sum=0L;
       int start=0;
       long mul=0L;
       long ans=0;
       long maxi[]=new long[n+1];
       for(int i=0;i<n;i++) {
    	   sum+=a[i];
    	   if(sum<0) {
    		   sum=0;
    		   if(d>0 && i!=0) {
    			   ans=Math.max(ans, pre[i-1]+(d-1)*mul);
    		   }
    		   ans=Math.max(ans,(i!=0)?pre[i-1]:0);
    		   pre[i]=sum;
    		   mul=sum;
    	   }
    	   else
    	   {
    		   pre[i]=sum;
    		   if(pre[i]>mul) {
    			   mul=pre[i];
    		   }
    		   if(d>0) {
    			   ans=Math.max(ans, pre[i]+(d-1)*mul);
    		   }
    	   }
    	   if(i!=0)
    	   maxi[i]=Math.max(maxi[i-1], pre[i]);
    	   else
    		   maxi[i]=pre[i];
       }
       if(d>0) {
		   ans=Math.max(ans, pre[n-1]+(d-1)*mul);
	   }
       ans=Math.max(ans, pre[n-1]);
	   long fi=0;

      
       
       sum=0L;
       for(int i=n-1;i>=0;i--) {
    	   sum+=a[i];
    	   if(sum<0) {
    		   sum=0;
    		   if(a[i]>0) {
    			   sum=a[i];
    		   }
    		   suf[i]=sum;
    	   }
    	   else
    	   {
    		   suf[i]=sum;
    	   }
       }
       if(d==0) {
    	   for(int i=n-1;i>=0;i--) {
    		  ans=Math.max(ans,maxi[i]+suf[i+1]);
    	   }
       }
       start=-1;
       if(d<0) {
    	   sum=0L;
    	   long got=0L;
    	   for(int i=0;i<n;i++) {
    		  sum+=a[i];
    		 if(sum>0) {
    			 sum=0;
    			 got=0;
    			 start=-1;
    		 }
    		 else{
    			 if(start==-1) {
    				 start=i-1;
    				 if(start!=-1)
    				 got=pre[start];
    			 }
    			 if(got+sum*d<pre[i]) {
    				 got=pre[i];
    				 start=i;
    				 sum=0;
    			 }
        		 ans=Math.max(ans,sum*d+((start!=-1)?pre[start]:0)+((i!=n-1)?suf[i+1]:0));
    		 }
    	   }
       }
       pw.println(ans);
       
       pw.flush();
       pw.close();
        
    }
         private static void debug(Object... o) {
     		System.out.println(Arrays.deepToString(o));
     	}
        static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        { 
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
        static class tri implements Comparable<tri> {
            int p, c, l;
 
            tri(int p, int c, int l) {
                this.p = p;
                this.c = c;
                this.l = l;
            }
 
            public int compareTo(tri o) {
                return Integer.compare(l, o.l);
            }
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
        public static long mod = 1000000007;
        public static int d;
        public static int p;
        public static int q;
        
        public static int[] suffle(int[] a,Random gen)
        {
            int n = a.length;
            for(int i=0;i<n;i++)
            {
                int ind = gen.nextInt(n-i)+i;
                int temp = a[ind];
                a[ind] = a[i];
                a[i] = temp;
            }
            return a;
        }
        
        public static void swap(int a, int b){
            int temp = a;
            a = b;
            b = temp;
        }
        
      
        
        public static void sieve(boolean[] isPrime,int n)
        {
            for(int i=1;i<n;i++)
                isPrime[i] = true;
            
            isPrime[0] = false;
            isPrime[1] = false;
            
            for(int i=2;i*i<n;i++)
            {
                if(isPrime[i] == true)
                {
                    for(int j=(2*i);j<n;j+=i)
                        isPrime[j] = false;
                }
            }
        }
        
        public static int GCD(int a,int b)
        {
            if(b==0)
                return a;
            else
                return GCD(b,a%b);
        }
        
        public static long GCD(long a,long b)
        {
            if(b==0)
                return a;
            else
                return GCD(b,a%b);
        }
        
        public static void extendedEuclid(int A,int B)
        {
            if(B==0)
            {
                d = A;
                p = 1 ;
                q = 0;
            }
            else
            {
                extendedEuclid(B, A%B);
                int temp = p;
                p = q;
                q = temp - (A/B)*q;
            }
        }
        
        public static long LCM(long a,long b)
        {
            return (a*b)/GCD(a,b);
        }
        
        public static int LCM(int a,int b)
        {
            return (a*b)/GCD(a,b);
        }
        
        public static int binaryExponentiation(int x,int n)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static long binaryExponentiation(long x,long n)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static int modularExponentiation(int x,int n,int M)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result * x)%M;
                x=(x%M*x)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modularExponentiation(long x,long n,long M)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result%M * x%M)%M;
                x=(x%M * x%M)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modInverse(int A,int M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static long modInverse(long A,long M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static boolean isPrime(int n)
        {
            
            if (n <= 1)  return false;
            if (n <= 3)  return true;
            
            if (n%2 == 0 || n%3 == 0) 
                return false;
         
            for (int i=5; i*i<=n; i=i+6)
            {
                if (n%i == 0 || n%(i+2) == 0)
                   return false;
            }
            
            return true;
        }
        
         public static long[] shuffle(long[] a, Random gen){ 
                for(int i = 0, n = a.length;i < n;i++){ 
                    int ind = gen.nextInt(n-i)+i; 
                    long d = a[i]; 
                    a[i] = a[ind]; 
                    a[ind] = d; 
                } 
                return a; 
            }
         static class pair implements Comparable<pair>{
             Long x;
             Integer y;
             pair(long sum,int id){
                 this.x=sum;
                 this.y=id;
             }
              public int compareTo(pair o) {
                     int result = x.compareTo(o.x);
                     if(result==0)
                         result = y.compareTo(o.y);
                     
                 return result;
                 }  
              public String toString(){
                 return (x+" "+y);
             }
       }       
        static class query{
        	Long x;
        	Integer y;
        	query(long x,int y){
        		this.x=x;
        		this.y=y;
        	}
        	public String toString(){
                return (x+" "+y);
            }
        }
      
}