| [DJ Genki vs Gram - Einherjar Joker](https://soundcloud.com/leon- hwang-368077289/einherjar-joker-dj-genki-vs-gram) | |
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| You have some cards. An integer between $1$ and $n$ is written on each card: specifically, for each $i$ from $1$ to $n$, you have $a_i$ cards which have the number $i$ written on them. | |
| There is also a shop which contains unlimited cards of each type. You have $k$ coins, so you can buy at most $k$ new cards in total, and the cards you buy can contain any integer between $\mathbf{1}$ and $\mathbf{n}$, inclusive. | |
| After buying the new cards, you must partition all your cards into decks, according to the following rules: | |
| * all the decks must have the same size; * there are no pairs of cards with the same value in the same deck. | |
| Find the maximum possible size of a deck after buying cards and partitioning them optimally. | |
| Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows. | |
| The first line of each test case contains two integers $n$, $k$ ($1 \leq n \leq 2 \cdot 10^5$, $0 \leq k \leq 10^{16}$) — the number of distinct types of cards and the number of coins. | |
| The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \leq a_i \leq 10^{10}$, $\sum a_i \geq 1$) — the number of cards of type $i$ you have at the beginning, for each $1 \leq i \leq n$. | |
| It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$. | |
| For each test case, output a single integer: the maximum possible size of a deck if you operate optimally. | |
| In the first test case, you can buy one card with the number $1$, and your cards become $[1, 1, 1, 1, 2, 2, 3, 3]$. You can partition them into the decks $[1, 2], [1, 2], [1, 3], [1, 3]$: they all have size $2$, and they all contain distinct values. You can show that you cannot get a partition with decks of size greater than $2$, so the answer is $2$. | |
| In the second test case, you can buy two cards with the number $1$ and o |