CF1883C Raspberries

You are given an array of integers $ a_1, a_2, \ldots, a_n $ and a number $ k $ ( $ 2 \leq k \leq 5 $ ). In one operation, you can do the following: - Choose an index $ 1 \leq i \leq n $ , - Set $ a_i = a_i + 1 $ . Find the minimum number of operations needed to make the product of all the numbers in the array $ a_1 \cdot a_2 \cdot \ldots \cdot a_n $ divisible by $ k $ .

Each test consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. Then follows the description of the test cases. The first line of each test case contains two integers $ n $ and $ k $ ( $ 2 \leq n \leq 10^5 $ , $ 2 \leq k \leq 5 $ ) — the size of the array $ a $ and the number $ k $ . The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_i \leq 10 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output the minimum number of operations needed to make the product of all the numbers in the array divisible by $ k $ .

In the first test case, we need to choose the index $ i = 2 $ twice. After that, the array will be $ a = [7, 5] $ . The product of all the numbers in the array is $ 35 $ . In the fourth test case, the product of the numbers in the array is $ 120 $ , which is already divisible by $ 5 $ , so no operations are needed. In the eighth test case, we can perform two operations by choosing $ i = 2 $ and $ i = 3 $ in any order. After that, the array will be $ a = [1, 6, 10] $ . The product of the numbers in the array is $ 60 $ .