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 $$$a_i \gt a_j$$$. 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?

Input

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 $$$2 \cdot 10^5$$$.

Output

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).

Note

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 $$$[500000001, 500000000]$$$.

Block Towers

Examples