A. K-divisible Sum
binary search; constructive algorithms; greedy; math
You are given two integers \(n\) and \(k\).You should create an array of \(n\) positive integers \(a_1, a_2, \dots, a_n\) such that the sum \((a_1 + a_2 + \dots + a_n)\) is divisible by \(k\) and maximum element in \(a\) is minimum possible.What is the minimum possible maximum element in \(a\)?
The first line contains a single integer \(t\) (\(1 \le t \le 1000\)) — the number of test cases.The first and only line of each test case contains two integers \(n\) and \(k\) (\(1 \le n \le 10^9\); \(1 \le k \le 10^9\)).
For each test case, print one integer — the minimum possible maximum element in array \(a\) such that the sum \((a_1 + \dots + a_n)\) is divisible by \(k\).
In the first test case \(n = 1\), so the array consists of one element \(a_1\) and if we make \(a_1 = 5\) it will be divisible by \(k = 5\) and the minimum possible.In the second test case, we can create array \(a = [1, 2, 1, 2]\). The sum is divisible by \(k = 3\) and the maximum is equal to \(2\).In the third test case, we can create array \(a = [1, 1, 1, 1, 1, 1, 1, 1]\). The sum is divisible by \(k = 8\) and the maximum is equal to \(1\).