CF1629B.GCD Arrays

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).

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 $4$ .