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)](https://en.wikipedia.org/wiki/Greatest_common_divisor) 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 $ .