Suppose you have a list of integers, and a move is defined as taking one of the integers from the list and replacing it with its square root, rounded down to the nearest integer.

Given an integer l and an integer k, start with the array [1, 2, 3 ... l] and find the minimal sum of the array after k moves.

Example

For l = 5 and k = 2, the output should be squareRoots(l, k) = 10.

We start with [1, 2, 3, 4, 5].

After square rooting 5 to get [1, 2, 3, 4, 2] and then square rooting 3 to get[1, 2, 1, 4, 2], we end up with a sum of 10.

Constraints

1 ≤ l ≤ 10⁴

1 ≤ k ≤ 10⁴

T = 10000

Input

The first line contains T the number of test cases followed by 2×T lines containing l and k.

Output

For every test case, output one line containing an integer, i.e. the minimal possible sum.

Sample

Input:
2
5
2
2327
4895

Output:
10
10647