[Solution] Difference of GCDs Codeforces Solution

B. Difference of GCDs

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given three integers n$n$, l$l$, and r$r$. You need to construct an array a1,a2,…,an$a_1,a_2,\dots ,a_n$ (l≤ai≤r$l\le a_i\le r$) such that gcd(i,ai)$gcd(i,a_i)$ are all distinct or report there's no solution.

Here gcd(x,y)$gcd(x,y)$ denotes the greatest common divisor (GCD) of integers x$x$ and y$y$.

Input

The input consists of multiple test cases. The first line contains a single integer t$t$ (1≤t≤104$1\le t\le {10}^4$) — the number of test cases. The description of the test cases follows.

The first line contains three integers n$n$, l$l$, r$r$ (1≤n≤105$1\le n\le {10}^5$, 1≤l≤r≤109$1\le l\le r\le {10}^9$).

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It is guaranteed that the sum of n$n$ over all test cases does not exceed 105${10}^5$.

Output

For each test case, if there is no solution, print "NO" (without quotes). You can print letters in any case (upper or lower).

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Otherwise, print "YES" (without quotes). In the next line, print n$n$ integers a1,a2,…,an$a_1,a_2,\dots ,a_n$ — the array you construct.

If there are multiple solutions, you may output any.