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B. GCD Arrays

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputConsider 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 $$$t$$$ ($$$1 \le t \le 10^5$$$) — 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).

Example

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

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 $$$4$$$.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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