A. Treasure Hunt
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Little B and his friend Little K found a treasure map, and now they just need to dig up the treasure, which is buried at a depth of $$$a.5$$$ meters.

They take turns digging. On the first day, Little B digs; on the second day, Little K. After each day, they switch. Little B digs exactly $$$x$$$ meters of soil each day, while Little K digs $$$y$$$ meters. They became curious about who will dig up the treasure first, meaning during whose day the total dug depth will exceed $$$a.5$$$.

But they are too busy digging, so help them and tell who will dig up the treasure!

Input

The first line contains an integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. The description of the test cases follows.

In a single line of each test case, three integers $$$x, y, a$$$ are given ($$$1 \leq x, y, a \leq 10^9$$$).

Output

For each test case, output "NO" if Little B digs it up first; otherwise, output "YES". You can output the answer in any case.

Example
Input
3
1 2 4
2 1 4
2 2 1
Output
YES
NO
NO
Note

In the first test case, on the first day they will dig $$$1$$$ meter; on the second day $$$1 + 2 = 3$$$ meters in total; on the third day $$$1 + 2 + 1 = 4$$$ meters; and on the fourth day they will dig $$$6$$$ meters. Thus, the treasure will be dug up first by Little K.

In the second test case, on the first day they will dig $$$2$$$ meters; on the second day $$$2 + 1 = 3$$$ meters in total; on the third day $$$2 + 1 + 2 = 5$$$ meters, meaning it was dug up first by Little B.