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D. Beautiful Array

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$x$$$ ($$$1 \le n \le 3 \cdot 10^5, -100 \le x \le 100$$$) — the length of array $$$a$$$ and the integer $$$x$$$ respectively.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$-10^9 \le a_i \le 10^9$$$) — 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.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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