GCD Arrays

Description:

Input:

The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 10^5$$$) — the number of test cases. The description of test cases follows.

The input for each test case consists of a single line containing $$$3$$$ non-negative integers $$$l$$$, $$$r$$$, and $$$k$$$ ($$$1 \leq l \leq r \leq 10^9, \enspace 0 \leq k \leq r - l$$$).

Output:

For each test case, print "YES" if it is possible to have the GCD of the corresponding array greater than $$$1$$$ by performing at most $$$k$$$ operations, and "NO" otherwise (case insensitive).

Sample Input:

9
1 1 0
3 5 1
13 13 0
4 4 0
3 7 4
4 10 3
2 4 0
1 7 3
1 5 3

Sample Output:

NO
NO
YES
YES
YES
YES
NO
NO
YES

Note:

For the first test case, $$$a = [1]$$$, so the answer is "NO", since the only element in the array is $$$1$$$.

For the second test case the array is $$$a = [3, 4, 5]$$$ and we have $$$1$$$ operation. After the first operation the array can change to: $$$[3, 20]$$$, $$$[4, 15]$$$ or $$$[5, 12]$$$ all of which having their greatest common divisor equal to $$$1$$$ so the answer is "NO".

For the third test case, $$$a = [13]$$$, so the answer is "YES", since the only element in the array is $$$13$$$.

For the fourth test case, $$$a = [4]$$$, so the answer is "YES", since the only element in the array is $$$4$$$.