Description: The two versions are different problems. You may want to read both versions. You can make hacks only if both versions are solved. You are given two positive integers $$$n$$$, $$$m$$$. Calculate the number of ordered pairs $$$(a, b)$$$ satisfying the following conditions: - $$$1\le a\le n$$$, $$$1\le b\le m$$$; - $$$a+b$$$ is a multiple of $$$b \cdot \gcd(a,b)$$$. Input Format: 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 $$$n$$$, $$$m$$$ ($$$1\le n,m\le 2 \cdot 10^6$$$). It is guaranteed that neither the sum of $$$n$$$ nor the sum of $$$m$$$ over all test cases exceeds $$$2 \cdot 10^6$$$. Output Format: For each test case, print a single integer: the number of valid pairs. Note: In the first test case, only $$$(1,1)$$$ satisfies the conditions. In the fourth test case, $$$(1,1),(2,1),(2,2),(3,1),(4,1),(5,1),(6,1),(6,2),(6,3),(7,1),(8,1),(9,1),(10,1),(10,2)$$$ satisfy the conditions.