#P1828A. Divisible Array

    ID: 8483 Type: RemoteJudge 1000ms 256MiB Tried: 0 Accepted: 0 Difficulty: 3 Uploaded By: Tags>constructive algorithmsmath*800

Divisible Array

No submission language available for this problem.

Description

You are given a positive integer nn. Please find an array a1,a2,,ana_1, a_2, \ldots, a_n that is perfect.

A perfect array a1,a2,,ana_1, a_2, \ldots, a_n satisfies the following criteria:

  • 1ai10001 \le a_i \le 1000 for all 1in1 \le i \le n.
  • aia_i is divisible by ii for all 1in1 \le i \le n.
  • a1+a2++ana_1 + a_2 + \ldots + a_n is divisible by nn.

Each test contains multiple test cases. The first line contains the number of test cases tt (1t2001 \le t \le 200). The description of the test cases follows.

The only line of each test case contains a single positive integer nn (1n2001 \le n \le 200) — the length of the array aa.

For each test case, output an array a1,a2,,ana_1, a_2, \ldots, a_n that is perfect.

We can show that an answer always exists. If there are multiple solutions, print any.

Input

Each test contains multiple test cases. The first line contains the number of test cases tt (1t2001 \le t \le 200). The description of the test cases follows.

The only line of each test case contains a single positive integer nn (1n2001 \le n \le 200) — the length of the array aa.

Output

For each test case, output an array a1,a2,,ana_1, a_2, \ldots, a_n that is perfect.

We can show that an answer always exists. If there are multiple solutions, print any.

Sample Input 1

7
1
2
3
4
5
6
7

Sample Output 1

1
2 4
1 2 3
2 8 6 4
3 4 9 4 5
1 10 18 8 5 36
3 6 21 24 10 6 14

Note

In the third test case:

  • a1=1a_1 = 1 is divisible by 11.
  • a2=2a_2 = 2 is divisible by 22.
  • a3=3a_3 = 3 is divisible by 33.
  • a1+a2+a3=1+2+3=6a_1 + a_2 + a_3 = 1 + 2 + 3 = 6 is divisible by 33.

In the fifth test case:

  • a1=3a_1 = 3 is divisible by 11.
  • a2=4a_2 = 4 is divisible by 22.
  • a3=9a_3 = 9 is divisible by 33.
  • a4=4a_4 = 4 is divisible by 44.
  • a5=5a_5 = 5 is divisible by 55.
  • a1+a2+a3+a4+a5=3+4+9+4+5=25a_1 + a_2 + a_3 + a_4 + a_5 = 3 + 4 + 9 + 4 + 5 = 25 is divisible by 55.