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.*;

public class TaskD {

    public static void main(String[] args) throws IOException {

        new TaskD().go();
    }

    PrintWriter out;
    Reader in;
    BufferedReader br;

    TaskD() throws IOException {

        try {

            //br = new BufferedReader( new FileReader("input.txt") );
            in = new Reader("input.txt");
            out = new PrintWriter( new BufferedWriter(new FileWriter("output.txt")) );
        }
        catch (Exception e) {

            //br = new BufferedReader( new InputStreamReader( System.in ) );
            in = new Reader();
            out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );
        }
    }

    void go() throws IOException {

        int t = 1;
        while (t > 0) {
            solve();
            //out.println();
            t--;
        }

        out.flush();
        out.close();
    }

    int inf = 2000000000;
    int mod = 1000000007;
    double eps = 0.000000001;

    int n;
    int m;
    ArrayList<Integer>[] g;
    void solve() throws IOException {
        int n = in.nextInt();
        int x = in.nextInt();
        int[] a = in.nextIntArray(n);

        long[] dl = new long[n];

        int p = 0;
        long sum = 0;
        long ans = 0;
        for (int i = 0; i < n; i++) {
            sum += a[i];
            while (p <= i && sum <= 0) {
                sum -= a[p];
                p++;
            }

            dl[i] = sum;
            ans = Math.max(ans, dl[i]);
        }

        if (x > 0) {
            out.print(ans * x);
            return;
        }

        long[][] d =  new long[n][2];
        if (a[0] < 0) d[0][0] = (long) a[0] * x;
        for (int i = 1; i < n; i++) {
            d[i][0] = Math.max(d[i][0], dl[i - 1] + (long) a[i] * x);
            d[i][0] = Math.max(d[i][0], d[i - 1][0] + (long) a[i] * x);
            d[i][1] = Math.max(d[i][1], d[i - 1][0] + a[i]);
            d[i][1] = Math.max(d[i][1], d[i - 1][1] + a[i]);
        }

        for (int i = 0; i < n; i++)
            for (int j = 0; j < 2; j++)
                ans = Math.max(ans, d[i][j]);

        out.print(ans);
    }


    class Pair implements Comparable<Pair> {
        int a;
        int b;

        Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }

        public int compareTo(Pair p) {
            if (a != p.a)
                return Integer.compare(a, p.a);
            else
                return Integer.compare(b, p.b);
        }
    }

    class Item {

        int a;
        int b;
        int c;

        Item(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

    }

    class Reader {

        BufferedReader  br;
        StringTokenizer tok;

        Reader(String file) throws IOException {
            br = new BufferedReader( new FileReader(file) );
        }

        Reader() throws IOException {
            br = new BufferedReader( new InputStreamReader(System.in) );
        }

        String next() throws IOException {

            while (tok == null || !tok.hasMoreElements())
                tok = new StringTokenizer(br.readLine());
            return tok.nextToken();
        }

        int nextInt() throws NumberFormatException, IOException {
            return Integer.valueOf(next());
        }

        long nextLong() throws NumberFormatException, IOException {
            return Long.valueOf(next());
        }

        double nextDouble() throws NumberFormatException, IOException {
            return Double.valueOf(next());
        }


        String nextLine() throws IOException {
            return br.readLine();
        }

        int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        ArrayList<Integer>[] nextGraph(int n, int m) throws IOException {
            ArrayList<Integer>[] g = new ArrayList[n];
            for (int i = 0; i < n; i++)
                g[i] = new ArrayList<>();
            for (int i = 0; i < m; i++) {
                int x = nextInt() - 1;
                int y = nextInt() - 1;
                g[x].add(y);
                g[y].add(x);
            }

            return g;
        }

    }

}