A. Consecutive Sum Riddle
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Theofanis has a riddle for you and if you manage to solve it, he will give you a Cypriot snack halloumi for free (Cypriot cheese).

You are given an integer $$$n$$$. You need to find two integers $$$l$$$ and $$$r$$$ such that $$$-10^{18} \le l < r \le 10^{18}$$$ and $$$l + (l + 1) + \ldots + (r - 1) + r = n$$$.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first and only line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 10^{18}$$$).

Output

For each test case, print the two integers $$$l$$$ and $$$r$$$ such that $$$-10^{18} \le l < r \le 10^{18}$$$ and $$$l + (l + 1) + \ldots + (r - 1) + r = n$$$.

It can be proven that an answer always exists. If there are multiple answers, print any.

Example
Input
7
1
2
3
6
100
25
3000000000000
Output
0 1
-1 2 
1 2 
1 3 
18 22
-2 7
999999999999 1000000000001
Note

In the first test case, $$$0 + 1 = 1$$$.

In the second test case, $$$(-1) + 0 + 1 + 2 = 2$$$.

In the fourth test case, $$$1 + 2 + 3 = 6$$$.

In the fifth test case, $$$18 + 19 + 20 + 21 + 22 = 100$$$.

In the sixth test case, $$$(-2) + (-1) + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 25$$$.