1358D - The Best Vacation - CodeForces Solution

from sys import stdin
input = stdin.readline





def answer():

    prefix = [0]
    psum = [0]

    for i in range(n):

        prefix.append(prefix[-1] + a[i])
        psum.append(psum[-1] + (a[i] * (a[i] + 1))//2)


    ans = 0
    for i in range(n):

        l , h = i + 1 , 2 * n
        val , sub , upper = 0 , 0 , i
        while(l <= h):

            mid = (l + h) // 2

            if(mid <= n):value = prefix[mid] - prefix[i]
            else:value = prefix[n] - prefix[i] + prefix[mid - n]
            
            if(value <= d):
                
                if(mid <= n):val = psum[mid] - psum[i]
                else:val = psum[n] - psum[i] + psum[mid - n]

                sub = value
                upper = mid
                
                l = mid + 1
            else:
                h = mid - 1


        req = d - sub
        if(req == 0):
            ans = max(ans , val)
            continue

        upper %= n

        buffer = a[upper] - req
        val += (a[upper] * (a[upper] + 1))//2
        val -= (buffer * (buffer + 1))//2

        ans = max(ans , val)
        
    return ans

     
for T in range(1):

    n , d = map(int,input().split())

    a = list(map(int,input().split()))

    print(answer())