Maximum Median

Description:
You are given an array a of n integers, where n is odd. You can make the following operation with it:

Choose one of the elements of the array (for example ai) and increase it by 1 (that is, replace it with ai+1).
You want to make the median of the array the largest possible using at most k operations.

The median of the odd-sized array is the middle element after the array is sorted in non-decreasing order. For example, the median of the array [1,5,2,3,5] is 3.

Input
The first line contains two integers n and k (1≤n≤2⋅1e5, n is odd, 1≤k≤1e9) — the number of elements in the array and the largest number of operations you can make.

The second line contains n integers a1,a2,…,an (1≤ai≤1e9).

Output
Print a single integer — the maximum possible median after the operations.

Examples
input
3 2
1 3 5
output
5
input
5 5
1 2 1 1 1
output
3
input
7 7
4 1 2 4 3 4 4
output
5
Note
In the first example, you can increase the second element twice. Than array will be [1,5,5] and it's median is 5.

In the second example, it is optimal to increase the second number and than increase third and fifth. This way the answer is 3.

In the third example, you can make four operations: increase first, fourth, sixth, seventh element. This way the array will be [5,1,2,5,3,5,5] and the median will be 5.

Problem solving:

Code:

#include <iostream>
#include <algorithm>
using namespace std;
const int maxn = 2e5 + 10;
typedef long long ll;
ll        a[maxn], n, k, mid;
bool check(ll x)
{
ll s = 0;
for (ll i = mid; i <= n; i++)
{
if (a[i] < x)
s += (x - a[i]);
if (k < s)
return 0;
}
return 1;
}
int main()
{
cin >> n >> k;
for (int i = 1; i <= n; i++)
cin >> a[i];
sort(a + 1, a + n + 1);
mid = (1 + n) >> 1;
ll l, r;
l = a[mid], r = a[mid] + k;
while (l <= r)
{
ll m = (l + r) >> 1;
if (check(m))
{
l = m + 1;
}
else
r = m - 1;
}
cout << l - 1 << endl;
}