CF2039A Shohag Loves Mod

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 $ .

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 $ ).

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.

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.