13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T647,

You are given a single integer $$$n.$$$ Construct an array of $$$n$$$ distinct positive integers $$$a_1, \ldots, a_n$$$ such that for all $$$i \, (1 \le i \le n)$$$, $$$a_1 + a_2 + a_3 + \ldots + a_n$$$ is divisible by $$$a_i,$$$ or determine that no such array exists.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 50$$$). The description of the test cases follows.

The first and only line of each test case contains a single integer $$$n \, (1 \le n \le 50).$$$

Output

For each test case, if there is no solution, output a single integer $$$-1$$$.

Otherwise, output $$$n$$$ integers $$$a_1, \ldots, a_n \, (1 \le a_i \le 10^{17})$$$ — an array satisfying the conditions.

If there are multiple solutions, print any of them.

Note

In the first test case, the cond

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Examples