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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 1a1<a2<<an100 such that aimod ^{\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.