D. Devilish Game
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You play a number game that your suspicious opponent recently learned about. The problem is: if you lose, you may also lose your soul, so it's quite important to win!

The rules of the game are quite simple: there are two positive integers $$$A$$$ and $$$B$$$ and a number $$$k$$$. Players take turns, starting with you. On their turn, a player can perform exactly one of two actions:

  • Subtract an integer from $$$1$$$ to $$$k$$$ from the number $$$A$$$;
  • Add an integer from $$$1$$$ to $$$k$$$ to the number $$$B$$$.

At the same time, during the game, the numbers $$$A$$$ and $$$B$$$ must remain positive; if a player makes a move that causes one of the numbers to become non-positive, they lose. The player who makes a move such that the sum of the numbers $$$A$$$ and $$$B$$$ becomes a prime number wins the game.

Can you win regardless of your opponent's actions?

Input

Each test contains several sets of input data. The first line of input contains a single integer $$$t$$$ — the number of sets of input data ($$$1 \leq t \leq 10$$$).

The following $$$t$$$ lines describe the sets of input data: each consists of one line containing three integers $$$A$$$, $$$B$$$, $$$k$$$ — the numbers $$$A$$$ and $$$B$$$ at the start of the game and the number $$$k$$$ ($$$1 \leq A, B, k \leq 10^9$$$).

It is guaranteed that $$$A + B$$$ is initially not a prime number.

Output

For each set of input data, output on a separate line "Yes" if you can win with the given initial data, and "No" otherwise.

Example
Input
4
1 7 2
3 5 2
3 6 1
253309356 182963670 154154154
Output
No
Yes
No
Yes