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 A {

    public static void main(String[] args) {
        FastReader scan = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        Task solver = new Task();
        int t = 1;
        while (t --> 0) solver.solve(1, scan, out);
        out.close();
    }

    static class Task {

        public void solve(int testNumber, FastReader scan, PrintWriter out) {
            int n = scan.nextInt();
            long x = scan.nextLong();
            long[] a = new long[n];
            long[][][] dp = new long[n][2][2];
            //dp[i][j][k] -> i = current index, j = do I plan on multiplying by x, k = have I multiplied by x before
            for(int i = 0; i < n; i++) a[i] = scan.nextLong();
            dp[0][0][0] = a[0];
            dp[0][1][0] = dp[0][1][1] = dp[0][0][1] = a[0]*x;
            for(int i = 1; i < n; i++) {
                dp[i][0][0] = Math.max(dp[i-1][0][0], 0) + a[i];
                dp[i][0][1] = Math.max(Math.max(Math.max(dp[i-1][0][1], dp[i-1][1][1]), dp[i-1][1][0]), 0) + a[i];
                dp[i][1][0] = Math.max(dp[i-1][0][0], 0) + a[i]*x;
                dp[i][1][1] = Math.max(Math.max(dp[i-1][1][0], dp[i-1][1][1]), 0) + a[i]*x;
            }
            long ans = 0;
            for(int i = 0; i < n; i++) {
                for(int j = 0; j < 2; j++) {
                    for(int k = 0; k < 2; k++) ans = Math.max(ans, dp[i][j][k]);
                }
            }
            out.println(ans);
        }
    }

    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static void shuffle(long[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            long temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(new File(s)));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}