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