Prefix Permutation Sums

Description:

Input:

The first line contains a positive number $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of the description of each test case contains a positive number $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the size of the initial array.

The second line of the description of each test case contains $$$n - 1$$$ positive number $$$a_i$$$ ($$$1 \le a_i \le 10^{18}$$$), $$$a_{i-1} < a_i$$$ — elements of the array of prefix sums.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, output "YES" if such a permutation exists, and "NO" otherwise.

You can output "YES" and "NO" in any case (for example, the strings "yEs", "yes" and "Yes" will be recognized as a positive response).

Sample Input:

12
5
6 8 12 15
5
1 6 8 15
4
1 2 100
4
1 3 6
2
2
3
1 2
4
3 7 10
5
5 44 46 50
4
1 9 10
5
13 21 36 42
5
1 2 3 1000000000000000000
9
9 11 12 20 25 28 30 33

Sample Output:

YES
YES
NO
YES
YES
NO
YES
NO
NO
NO
NO
NO

Note:

In the fourth example, for example, the permutation $$$[1, 2, 3, 4]$$$ is suitable. In the fifth example, for example, the permutation $$$[2, 1]$$$ is suitable. In the seventh example, for example, the permutation $$$[1, 2, 4, 3]$$$ is suitable.