Given N, print a sequence of Npositive integers A1,A2,…,AN that satisfy the following conditions:
∑i=1NAi=lcm(A1,A2,…,AN)
1≤Ai≤109
If there exists no such sequence, print −1.
lcm denotes the least common multiple. The least common multiple of some positive integers is the least positive integer which is multiple for each of them.
Input
The first line of each test case contains an integer T(1≤T≤100)— the number of test cases.
Each of the next T lines will contain an integer N(1≤N≤105)— the length of the sequence.
Sum of N over all test cases does not exceed 106.
Output
For each test case, print N space separated positive integers that satisfy the given conditions on a separate line. If there exists no such sequence, print −1.
If there are multiple sequences that satisfy the conditions, you can output any of them.