A. Shohag Loves Mod
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Shohag has an integer $$$n$$$. Please help him find an increasing integer sequence $$$1 \le a_1 \lt a_2 \lt \ldots \lt a_n \le 100$$$ such that $$$a_i \bmod i \neq a_j \bmod j$$$ $$$^{\text{∗}}$$$ is satisfied over all pairs $$$1 \le i \lt j \le n$$$.

It can be shown that such a sequence always exists under the given constraints.

$$$^{\text{∗}}$$$$$$a \bmod b$$$ denotes the remainder of $$$a$$$ after division by $$$b$$$. For example, $$$7 \bmod 3 = 1, 8 \bmod 4 = 0$$$ and $$$69 \bmod 10 = 9$$$.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 50$$$) — the number of test cases.

The first and only line of each test case contains an integer $$$n$$$ ($$$2 \le n \le 50$$$).

Output

For each test case, print $$$n$$$ integers — the integer sequence that satisfies the conditions mentioned in the statement. If there are multiple such sequences, output any.

Example
Input
2
3
6
Output
2 7 8
2 3 32 35 69 95
Note

In the first test case, the sequence is increasing, values are from $$$1$$$ to $$$100$$$ and each pair of indices satisfies the condition mentioned in the statement:

  • For pair $$$(1, 2)$$$, $$$a_1 \bmod 1 = 2 \bmod 1 = 0$$$, and $$$a_2 \bmod 2 = 7 \bmod 2 = 1$$$. So they are different.
  • For pair $$$(1, 3)$$$, $$$a_1 \bmod 1 = 2 \bmod 1 = 0$$$, and $$$a_3 \bmod 3 = 8 \bmod 3 = 2$$$. So they are different.
  • For pair $$$(2, 3)$$$, $$$a_2 \bmod 2 = 7 \bmod 2 = 1$$$, and $$$a_3 \bmod 3 = 8 \bmod 3 = 2$$$. So they are different.

Note that you do not necessarily have to print the exact same sequence, you can print any other sequence as long as it satisfies the necessary conditions.