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: - $$$1\le a\le n$$$, $$$1\le b\le m$$$; - $$$b \cdot \gcd(a,b)$$$ is a multiple of $$$a+b$$$. 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, no pair satisfies the conditions. In the fourth test case, $$$(2,2),(3,6),(4,4),(6,3),(6,6),(8,8)$$$ satisfy the conditions.