B"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 k new cards in total, and the cards you buy can contain any integer between 1 and n . After buying the new cards, you rearrange all your cards in a line. The score of a rearrangement is the number of (contiguous) subarrays of length n which are a permutation of [1, 2, ldots, n] . What's the maximum score you can get? Each test contains multiple test cases. The first line contains the number of test cases t (1 <= t <= 100) . The description of the test cases follows. The first line of each test case contains two integers n , k ( 1 <= n <= 2 cdot 10^5 , 0 <= k <= 10^{12} ) -- 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 ( 1 <= a_i <= 10^{12} ) -- the number of cards of type i you have at the beginning. It is guaranteed that the sum of n over all test cases does not exceed 5 cdot 10^5 . For each test case, output a single line containing an integer: the maximum score you can get. In the first test case, the final (and only) array we can get is [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (including 11 single 1 s), which contains 11 subarrays consisting of a permutation of [1] . In the second test case, we can buy 0 cards of type 1 and 4 cards of type 2 , and then we rearrange the cards as following: [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2] . There are 8 subarrays equal to [1, 2] and 7 subarrays equal to [2, 1] , which make a total of 15 subarrays which are a permutation of [1"...