B. GCD Arrays
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

The first line of the input contains a single integer t (1≤t≤105) — 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≤l≤r≤109,0≤k≤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).

Example
Input
Copy
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
Output
Copy
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.