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 tr1 {
	static PrintWriter out;
	static StringBuilder sb;
	static int n;
	static long x;
	static int[] a;
	static long memo[][][];

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		n = sc.nextInt();
		x = sc.nextInt();
		a=new int [n];
		for (int i = 0; i < n; i++)
			a[i] = sc.nextInt();
		memo = new long[n][3][3];
		for(long [][]h:memo)
			for(long[]a:h)
				Arrays.fill(a, -1);
		out.println(dp(0,0,0));
		out.flush();
	}

	static long dp(int i, int ma, int ml) {
		if (i == n)
			return 0;
		if (memo[i][ma][ml] != -1)
			return memo[i][ma][ml];
		long ans = -(long) 1e9;
		if(ma==0) {
			ans=Math.max(ans, dp(i+1,0,0));
			if(ml==0) {
				ans=Math.max(ans,dp(i+1,1,0)+a[i]);
				ans=Math.max(ans, dp(i+1,1,1)+a[i]*x);
				ans=Math.max(ans, dp(i+1,1,2)+a[i]);
			}
			ans=Math.max(ans, dp(i+1,2,0));
		}
		if(ma==1) {
			if(ml==0) {
			ans=Math.max(ans, dp(i+1,1,0)+a[i]);
			ans=Math.max(ans, dp(i+1,1,1)+a[i]*x);
			ans=Math.max(ans, dp(i+1,1,2)+a[i]);
	     	}
			if(ml==1) {
				ans=Math.max(ans, dp(i+1,1,1)+a[i]*x);
				ans=Math.max(ans, dp(i+1,1,2)+a[i]);
			}
			if(ml==2)
			ans=Math.max(ans, dp(i+1,1,2)+a[i]);
			ans=Math.max(ans, dp(i+1,2,0));
		}
		if(ma==2)
			ans=Math.max(ans,dp(i+1,2,0));
		return memo[i][ma][ml]=ans;
	}

	static long mod = (long) 1e9 + 7;
	static long[] fact;

	static void fac(int n) {
		fact[0] = 1;
		for (int i = 1; i <= n; i++)
			fact[i] = (1l * i * fact[i - 1]) % mod;
	}

	static int gcd(int a, int b) {

		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	static class unionfind {
		int[] p;
		int[] size;

		unionfind(int n) {
			p = new int[n];
			size = new int[n];

			for (int i = 0; i < n; i++) {
				p[i] = i;
			}
			Arrays.fill(size, 1);
		}

		int findSet(int v) {
			if (v == p[v])
				return v;
			return p[v] = findSet(p[v]);
		}

		boolean sameSet(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			return false;
		}

		int max() {
			int max = 0;
			for (int i = 0; i < size.length; i++)
				if (size[i] > max)
					max = size[i];
			return max;
		}

		void combine(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return;
			if (size[a] > size[b]) {
				p[b] = a;
				size[a] += size[b];

			} else {
				p[a] = b;
				size[b] += size[a];
			}
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}