1155_D. Beautiful Array
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.
```python
import sys

#Library Info(ACL for Python/Pypy) -> https://github.com/not522/ac-library-python

def input():
    return sys.stdin.readline().rstrip()

DXY = [(0, -1), (1,0), (0, 1), (-1,0)] #L,D,R,Uの順番

INF = 1 << 64

def main():
    n,x = map(int,input().split())
    a = list(map(int,input().split()))
    A = [0] + a.copy()
    revA = [0] + a.copy()[::-1]
    b = [-INF]*(n)
    revb = [-INF]*(n)
    ans = 0

    #case 1. do not multiply

    for i in range(1,n + 1):
        A[i] += A[i - 1]
        revA[i] += revA[i - 1]

    for i in range(1,n + 1):
        ans = max(A[i] - A[i - 1],ans)
        b[i - 1] = max(A[i] - A[i - 1],0)
        revb[i - 1] = max(revA[i] - revA[i - 1],0)
        A[i] = min(A[i],A[i - 1])
        revA[i] = min(revA[i],revA[i - 1])

    #b[i] := (-inf,i]での部分和最大値(とらないのもあり)

    #case 2. multiply
    dp0 = [-INF]*(n) #dp0[i] := (-inf,i)でiまでにx倍しているときの最大値
    for i in range(n):
        if i > 0:
            dp0[i] = max(dp0[i - 1] + x * a[i],b[i - 1] + x * a[i])
        else:
            dp0[i] = x * a[i]

    dp1 = [-INF]*(n) #dp0のa[::-1]ver
    for i in range(n):
        if i > 0:
            dp1[i] = max(dp1[i - 1] + x * a[n - 1 - i],revb[i - 1] + x * a[n - 1 - i])
        else:
            dp1[i] = x * a[n - 1 - i]
    
    for i in range(n):
        ans = max(ans,dp0[i] + dp1[n - 1 - i] - x * a[i])
    print(ans)
    return 0


if __name__ == "__main__":
    main()

```