Candy Shop

现在有 $m$ 个包裹，第 $i$ 个包裹中包含 $i$ 个水晶，并且它的价格为 $i$ $n$ 个人需要按顺序购买包裹，其中第 $i$ 个人只有 $ai$ 的预算 购买的规则是这样的： - 从第一个人开始购买，每个人每次只能购买一个包裹。在第 $i$ $(i < n)$ 个人购买结束后第 $i + 1$ 个人开始购买，第 $n$ 个人购买结束后则又轮 到第一个人 - 当前购买者购买的包裹中包含的水晶个数必须严格比前一个人多 - 对于每个人来说，他购买的总金额不能超过他的预算 - 当最后一个人购买结束后所有人手中的包裹必须一样多 求这 $n$ 个人最多能购买多少水晶。若不存在一种合法的购买方案则输出 $0$ $n ≤ 200000$ $m ≤ 5000000$

The prestigious Codeforces kindergarten consists of $ n $ kids, numbered $ 1 $ through $ n $ . Each of them are given allowance in rubles by their parents. Today, they are going to the most famous candy shop in the town. The shop sells candies in packages: for all $ i $ between $ 1 $ and $ m $ , inclusive, it sells a package containing exactly $ i $ candies. A candy costs one ruble, so a package containing $ x $ candies costs $ x $ rubles. The kids will purchase candies in turns, starting from kid 1. In a single turn, kid $ i $ will purchase one candy package. Due to the highly competitive nature of Codeforces kindergarten, during a turn, the number of candies contained in the package purchased by the kid will always be strictly greater than the number of candies contained in the package purchased by the kid in the preceding turn (an exception is in the first turn: the first kid may purchase any package). Then, the turn proceeds to kid $ i+1 $ , or to kid $ 1 $ if it was kid $ n $ 's turn. This process can be ended at any time, but at the end of the purchase process, all the kids must have the same number of candy packages. Of course, the amount spent by each kid on the candies cannot exceed their allowance. You work at the candy shop and would like to prepare the candies for the kids. Print the maximum number of candies that can be sold by the candy shop to the kids. If the kids cannot purchase any candy (due to insufficient allowance), print $ 0 $ .

The first line contains two space-separated integers $ n $ and $ m $ $ (2<=n<=2·10^{5},2<=m<=5·10^{6},n<=m $ ), denoting the number of kids and the maximum number of candies in a package sold by the candy shop, respectively. Then $ n $ lines follow, each line will contain a single positive integer not exceeding  denoting the allowance of a kid in rubles. The allowances are given in order from kid $ 1 $ to kid $ n $ . Please, do not use the %lld specificator to read or write 64-bit integers in C++. It is recommended to use cin, cout streams (also you may use %I64d specificator).

Print a single integer denoting the maximum number of candies that can be sold by the candy shop.

2 5
5
10

13

3 8
8
16
13

32

2 5000000
12500002500000
12500002500000

12500002500000

For the first example, one of the scenarios that will result in $ 13 $ purchased candies is as follows. - Turn 1. Kid 1 purchases 1 candy. - Turn 2. Kid 2 purchases 3 candies. - Turn 3. Kid 1 purchases 4 candies. - Turn 4. Kid 2 purchases 5 candies.