Score : $300$ points

问题陈述

有 $N$ 个人参加一个活动，第 $i$ 个人的交通费用是 $A_i$ 日元。

活动组织者高桥决定设定一个交通补贴的最大限额 $x$。第 $i$ 个人的补贴将是 $\min(x, A_i)$ 日元。这里，$x$ 必须是一个非负整数。

已知高桥的预算是 $M$ 日元，他希望所有 $N$ 个人的总交通补贴最多为 $M$ 日元，那么补贴限额 $x$ 的最大可能值是多少？

如果补贴限额可以无限大，那么请报告这一点。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

There are $N$ people participating in an event, and the transportation cost for the $i$-th person is $A_i$ yen.

Takahashi, the organizer of the event, decided to set a maximum limit $x$ for the transportation subsidy. The subsidy for person $i$ will be $\min(x, A_i)$ yen. Here, $x$ must be a non-negative integer.

Given that Takahashi's budget is $M$ yen, and he wants the total transportation subsidy for all $N$ people to be at most $M$ yen, what is the maximum possible value of the subsidy limit $x$?

If the subsidy limit can be made infinitely large, report that instead.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq M \leq 2 \times 10^{14}$
• $1 \leq A_i \leq 10^9$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$ $M$

$A_1$ $A_2$ $\ldots$ $A_{N}$

Output

Print the maximum value of the subsidy limit $x$ that satisfies the budget condition, as an integer.

If the subsidy limit can be made infinitely large, print infinite instead.

Sample Input 1

4 8
1 3 2 4

Sample Output 1

2

If the subsidy limit is set to $2$ yen, the total transportation subsidy for all $N$ people is $\min(2,1) + \min(2,3) + \min(2,2) + \min(2,4) = 7$ yen, which is within the budget of $8$ yen.

If the subsidy limit is set to $3$ yen, the total transportation subsidy for all $N$ people is $\min(3,1) + \min(3,3) + \min(3,2) + \min(3,4) = 9$ yen, which exceeds the budget of $8$ yen.

Therefore, the maximum possible value of the subsidy limit is $2$ yen.

Sample Input 2

3 20
5 3 2

Sample Output 2

infinite

The subsidy limit can be made infinitely large.

Sample Input 3

10 23
2 5 6 5 2 1 7 9 7 2

Sample Output 3

2