Let's define the function
mex as follows:
mex(A) — is the minimum positive integer that is not in the set
A.
For example,
mex of set {1, 2, 3, 5, 100} is 4, and
mex of set {2, 3, 4, 5} is 1 .
You have a set of numbers
A, consisting of
n positive integers, and a positive number
k. Then you performed the following operation
k times: added to the set
A one more number equal to
mex(A), thereby increasing the size each time set
A by one.
Given a set
A and a number
k determine the last number that was added to the set.
Input
The first line contains two integers
n and
k (1<=n<=100000, 1<=k<=10
9) &mdash ; the number of numbers in the set and the number of addition operations.
The second line contains
n distinct integers
a1,
a2, ...,
an (1<=a
i<=100000) — elements of set A.
Imprint
Print a single integer — the last number that was added to the set.
Note
In the first example, the mex of the set {1, 2, 4, 5} is equal to 3, after adding mex to the set, it will become equal to {1, 2, 3, 4, 5}.
Examples
| # |
Input |
Output |
| 1 |
4 1
4 2 1 5
|
3
|
| 2 |
7 10
1 3 20 2 7 45 5
|
15
|