# Difference of GCDs Solution Codeforces

You are given three integers nnll, and rr. You need to construct an array a1,a2,,ana1,a2,…,an (lairl≤ai≤r) such that gcd(i,ai)gcd(i,ai) are all distinct or report there’s no solution.

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

## Input Difference of GCDs Solution Codeforces

The input consists of multiple test cases. The first line contains a single integer tt (1t1041≤t≤104) — the number of test cases. The description of the test cases follows.

The first line contains three integers nnllrr (1n1051≤n≤1051lr1091≤l≤r≤109).

It is guaranteed that the sum of nn over all test cases does not exceed 105105.

### Output Difference of GCDs Solution Codeforces

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

Otherwise, print “YES” (without quotes). In the next line, print nn integers a1,a2,,ana1,a2,…,an — the array you construct.

If there are multiple solutions, you may output any.

## Example Difference of GCDs Solution Codeforces

input

Copy
4
5 1 5
9 1000 2000
10 30 35
1 1000000000 1000000000

output

Copy
YES
1 2 3 4 5
YES
1145 1926 1440 1220 1230 1350 1001 1000 1233
NO
YES
1000000000


## Note Difference of GCDs Solution Codeforces

In the first test case, gcd(1,a1),gcd(2,a2),,gcd(5,a5)gcd(1,a1),gcd(2,a2),…,gcd(5,a5) are equal to 1122334455, respectively.