13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T662,

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

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

For each test case, print a single integer: the number

Reverse Card (Hard Version)

Examples