Block Towers
There are $$$n$$$ block towers, numbered from $$$1$$$ to $$$n$$$. The $$$i$$$-th tower consists of $$$a_i$$$ blocks.In one move, you can move one block from tower $$$i$$$ to tower $$$j$$$, but only if $$$a_i > a_j$$$. That move increases $$$a_j$$$ by $$$1$$$ and decreases $$$a_i$$$ by $$$1$$$. You can perform as many moves as you would like (possibly, zero).What's the largest amount of blocks you can have on the tower $$$1$$$ after the moves?
In the first testcase, you can move a block from tower $$$2$$$ to tower $$$1$$$, making the block counts $$$[2, 1, 3]$$$. Then move a block from tower $$$3$$$ to tower $$$1$$$, making the block counts $$$[3, 1, 2]$$$. Tower $$$1$$$ has $$$3$$$ blocks in it, and you can't obtain a larger amount.In the second testcase, you can move a block from any of towers $$$2$$$ or $$$3$$$ to tower $$$1$$$, so that it has $$$2$$$ blocks in it.In the third testcase, you can $$$500000000$$$ times move a block from tower $$$2$$$ to tower $$$1$$$. After that the block countes will be $$$[500000001, 500000000]$$$.
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of testcases.The first line of each testcase contains a single integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the number of towers.The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the number of blocks on each tower.The sum of $$$n$$$ over all testcases doesn't exceed $$$2 \cdot 10^5$$$.
For each testcase, print the largest amount of blocks you can have on the tower $$$1$$$ after you make any number of moves (possibly, zero).
from math import ceil

class Solution:

    def __init__(self):
        pass

    def solve(self):
        t = int(input())
        result = []
        for i in range(t):
            n = int(input())
            arr = list(map(int, input().split()))
            first = arr[0]
            arr.sort()
            for a in arr:
                if first < a:
                    first = ceil((first + a) / 2)
            result.append(first)
        for x in result:
            print(x)
if __name__ == '__main__':
    sol = Solution()
    sol.solve()
if __name__ == '__main__':
    result = []
    t = int(input())
    for _ in range(t):
        n = int(input())
        a = list(map(int, input().split()))
        prim = a[0]
        a = a[1:]
        a.sort()
        for i in range(n - 1):
            if a[i] > prim:
                x = (a[i] - prim + 1) // 2
                prim += x
        result.append(prim)
    for x in result:
        print(x)
a = int(input())
tests = []
for i in range(a):
    n = int(input())
    tests.append(list(map(int, input().split())))
for i in tests:
    ans = i[0]
    i.sort()
    for j in i:
        if j > ans:
            ans += (j - ans + 1) // 2
    print(ans)