GCD Arrays
Description
Consider the array $a$ composed of all the integers in the range $[l, r]$. For example, if $l = 3$ and $r = 7$, then $a = [3, 4, 5, 6, 7]$.
Given $l$, $r$, and $k$, is it possible for $\gcd(a)$ to be greater than $1$ after doing the following operation at most $k$ times?
- Choose $2$ numbers from $a$.
- Permanently remove one occurrence of each of them from the array.
- Insert their product back into $a$.
$\gcd(b)$ denotes the greatest common divisor (GCD) of the integers in $b$.
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 $k$ ($1 \leq l \leq r \leq 10^9, \enspace 0 \leq k \leq r - l$).
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).
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).
Samples
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
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 $4$.