After DSAA class, Jackie wants to buy lunch food.

There are n shops in a circle, which are labelled from 1 to n. Each shop has infinity food, and the price of the food at i-th shop is A_i. Jackie will start his shopping by following the circle “1 -> 2 -> 3 … -> n -> 1->2->...” to buy food. In i-th shop, if Jackie has enough money to buy one unit food in this shop, he will pay A_i to buy it and go to the next shop, otherwise he will go to the next shop. If he could not buy anything, he will stop shopping.

Now the money in Jackie’s pocket is m, he wants to know the total amount of food he can buy.

The first line contains two integers n, m (1 ≤ n ≤ 200000, 0 ≤ m ≤ 10¹⁸), denotes the number of the shop and the money Jackie has.

The second line contains n integers, the i-th integer A_i (1 ≤ A_i ≤ 10⁹) denotes the unit price of the food in i-th shop.

One line an integer, denotes the amount of food Jackie can buy.

Jackie will stop buying when he has paid 1+2+2+1=6. Thus, the total amount of food he can get is 4.