B. Prove Him Wrong
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Recently, your friend discovered one special operation on an integer array $$$a$$$:

  1. Choose two indices $$$i$$$ and $$$j$$$ ($$$i \neq j$$$);
  2. Set $$$a_i = a_j = |a_i - a_j|$$$.

After playing with this operation for a while, he came to the next conclusion:

  • For every array $$$a$$$ of $$$n$$$ integers, where $$$1 \le a_i \le 10^9$$$, you can find a pair of indices $$$(i, j)$$$ such that the total sum of $$$a$$$ will decrease after performing the operation.

This statement sounds fishy to you, so you want to find a counterexample for a given integer $$$n$$$. Can you find such counterexample and prove him wrong?

In other words, find an array $$$a$$$ consisting of $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) such that for all pairs of indices $$$(i, j)$$$ performing the operation won't decrease the total sum (it will increase or not change the sum).

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. Then $$$t$$$ test cases follow.

The first and only line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 1000$$$) — the length of array $$$a$$$.

Output

For each test case, if there is no counterexample array $$$a$$$ of size $$$n$$$, print NO.

Otherwise, print YES followed by the array $$$a$$$ itself ($$$1 \le a_i \le 10^9$$$). If there are multiple counterexamples, print any.

Example
Input
3
2
512
3
Output
YES
1 337
NO
YES
31 4 159
Note

In the first test case, the only possible pairs of indices are $$$(1, 2)$$$ and $$$(2, 1)$$$.

If you perform the operation on indices $$$(1, 2)$$$ (or $$$(2, 1)$$$), you'll get $$$a_1 = a_2 = |1 - 337| = 336$$$, or array $$$[336, 336]$$$. In both cases, the total sum increases, so this array $$$a$$$ is a counterexample.