BABA taught properties of right angled triangle and asked a questions: "Can you find a right angled triangle whose length of hypotenuse is H and its area is A?"

INDIAN students can answer quickly.

Input

The first line of the input contains a single integer T (where 1 ≤ T ≤ 10^5) denoting the number of test-cases. T test cases follow.

For each test case, there will be a single line containing two space separated integer H and A (where 1 ≤ H ≤ 10^6 and 1 ≤ A ≤ 10^12).

Output

Output the answer for each test-case in a single line. If it is not possible to find such a triangle, output -1.

Otherwise print 3 real numbers corresponding to the lengths of the sides of the triangle sorted in non-decreasing order.

NOTE: give your answer with 6 decimal places.

Example

Input:
4
24252 56578987908
1 1
2 2
10 10

Output:
-1
-1
-1
2.043096 9.789063 10.000000