CF1622C Set or Decrease

You are given an integer array $ a_1, a_2, \dots, a_n $ and integer $ k $ . In one step you can - either choose some index $ i $ and decrease $ a_i $ by one (make $ a_i = a_i - 1 $ ); - or choose two indices $ i $ and $ j $ and set $ a_i $ equal to $ a_j $ (make $ a_i = a_j $ ). What is the minimum number of steps you need to make the sum of array $ \sum\limits_{i=1}^{n}{a_i} \le k $ ? (You are allowed to make values of array negative).

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. The first line of each test case contains two integers $ n $ and $ k $ ( $ 1 \le n \le 2 \cdot 10^5 $ ; $ 1 \le k \le 10^{15} $ ) — the size of array $ a $ and upper bound on its sum. The second line of each test case contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le 10^9 $ ) — the array itself. It's guaranteed that the sum of $ n $ over all test cases doesn't exceed $ 2 \cdot 10^5 $ .

For each test case, print one integer — the minimum number of steps to make $ \sum\limits_{i=1}^{n}{a_i} \le k $ .

In the first test case, you should decrease $ a_1 $ $ 10 $ times to get the sum lower or equal to $ k = 10 $ . In the second test case, the sum of array $ a $ is already less or equal to $ 69 $ , so you don't need to change it. In the third test case, you can, for example: 1. set $ a_4 = a_3 = 1 $ ; 2. decrease $ a_4 $ by one, and get $ a_4 = 0 $ . As a result, you'll get array $ [1, 2, 1, 0, 1, 2, 1] $ with sum less or equal to $ 8 $ in $ 1 + 1 = 2 $ steps.In the fourth test case, you can, for example: 1. choose $ a_7 $ and decrease in by one $ 3 $ times; you'll get $ a_7 = -2 $ ; 2. choose $ 4 $ elements $ a_6 $ , $ a_8 $ , $ a_9 $ and $ a_{10} $ and them equal to $ a_7 = -2 $ . As a result, you'll get array $ [1, 2, 3, 1, 2, -2, -2, -2, -2, -2] $ with sum less or equal to $ 1 $ in $ 3 + 4 = 7 $ steps.