Kvass and the Fair Nut

Description:

Input:

The first line contains two integers $$$n$$$ and $$$s$$$ ($$$1 \le n \le 10^3$$$, $$$1 \le s \le 10^{12}$$$) — the number of kegs and glass volume.

The second line contains $$$n$$$ integers $$$v_1, v_2, \ldots, v_n$$$ ($$$1 \le v_i \le 10^9$$$) — the volume of $$$i$$$-th keg.

Output:

If the Fair Nut cannot pour his glass by $$$s$$$ liters of kvass, print $$$-1$$$. Otherwise, print a single integer — how much kvass in the least keg can be.

Sample Input:

3 3
4 3 5

Sample Output:

3

Sample Input:

3 4
5 3 4

Sample Output:

2

Sample Input:

3 7
1 2 3

Sample Output:

-1

Note:

In the first example, the answer is $$$3$$$, the Fair Nut can take $$$1$$$ liter from the first keg and $$$2$$$ liters from the third keg. There are $$$3$$$ liters of kvass in each keg.

In the second example, the answer is $$$2$$$, the Fair Nut can take $$$3$$$ liters from the first keg and $$$1$$$ liter from the second keg.

In the third example, the Fair Nut can't pour his cup by $$$7$$$ liters, so the answer is $$$-1$$$.