For two positive integers l and r (l ≤ r) let c(l, r) denote the number of integer pairs (i, j) such that l ≤ i ≤ j ≤ r and \operatorname{gcd}(i, j) ≥ l. Here, \operatorname{gcd}(i, j) is the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers i and j.

YouKn0wWho has two integers n and k where 1 ≤ k ≤ n. Let f(n, k) denote the minimum of ∑_{i=1}^{k}{c(x_i+1,x_{i+1})} over all integer sequences 0=x_1 < x_2 < … < x_{k} < x_{k+1}=n.

Help YouKn0wWho find f(n, k). 

Input

The first line contains a single integer t (1 ≤ t ≤ 3 ⋅ 10^5) — the number of test cases.

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

Output

For each test case, print a single integer — f(n, k).

Example

Input


4
6 2
4 4
3 1
10 3


Output


8
4
6
11

Note

In the first test case, YouKn0wWho can select the sequence [0, 2, 6]. So f(6, 2) = c(1, 2) + c(3, 6) = 3 + 5 = 8 which is the minimum possible.

Source: codeforces | Difficulty: VERY_HARD
Tags: Number theory

Dynamic programming

Divide and conquer


Solutions: