Codeforces Round 767 (Div. 2) |
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Finished |
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?
$$$\gcd(b)$$$ 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).
91 1 03 5 113 13 04 4 03 7 44 10 32 4 01 7 31 5 3
NO NO YES YES YES YES NO NO YES
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 $$$4$$$.
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