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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

Sample Output:
10
10647