bins are lined up in a row, numbered
to
from left to right. Bin
initially contains
balls, and it is considered beautiful if it contains
balls. In one move, you may pick a bin
with at least
balls, move one ball from bin
to any bin on its left, and move another ball from bin
to any bin on its right. After some sequence of moves, is it possible to make all of the bins beautiful? To ensure the integrity of your solution, there may be up to
test cases.
Constraints
The sum of over all test cases does not exceed
.
Input Specification
The first line contains a single integer , the number of test cases. The next
lines describe the test cases.
The first line of each test case contains a single integer .
The second line of each test case contains integers
.
The third line of each test case contains integers
.
Output Specification
For each test case, output a single line containing YES
if it is possible to make all of the bins beautiful or NO
otherwise.
Sample Input
2
5
2 4 4 2 1
4 3 1 3 2
5
1 1 2 4 2
4 3 4 1 3
Sample Output
YES
NO
Explanation for Sample
For the first test case, one possible solution is as follows:
- Move one ball from bin
to bin
and another from bin
to bin
. The number of balls in each bin is now
.
- Move one ball from bin
to bin
and another from bin
to bin
. The number of balls in each bin is now
.
- Move one ball from bin
to bin
and another from bin
to bin
. The number of balls in each bin is now
.
For the second test case, it can be proven that it is impossible to make all of the bins beautiful.
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