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:T69b,

For two positive integers $$$l$$$ and $$$r$$$ ($$$l \le r$$$) let $$$c(l, r)$$$ denote the number of integer pairs $$$(i, j)$$$ such that $$$l \le i \le j \le r$$$ and $$$\operatorname{gcd}(i, j) \ge l$$$. Here, $$$\operatorname{gcd}(i, j)$$$ is the greatest common divisor (GCD) of integers $$$i$$$ and $$$j$$$.

YouKn0wWho has two integers $$$n$$$ and $$$k$$$ where $$$1 \le k \le n$$$. Let $$$f(n, k)$$$ denote the minimum of $$$\sum\limits_{i=1}^{k}{c(x_i+1,x_{i+1})}$$$ over all integer sequences $$$0=x_1 \lt x_2 \lt \ldots \lt x_{k} \lt x_{k+1}=n$$$.

Help YouKn0wWho find $$$f(n, k)$$$.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 3 \cdot 10^5$$$) — the number of test cases.

The first and only line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 10^5$$$).

Output

Artistic Partition

Examples