A sequence a is an infinite arithmetic progression. You are given three integers: S, A, and B. It is known that the sum of the elements of the sequence from index A to index B inclusive is exactly S.
Your task is to find any pair of integers a_0 (the initial term) and d (the common difference) that satisfy this condition. If multiple solutions exist, you may output any of them. If no such integers exist, report that it is impossible.
Input
The first line contains an integer T (1 \le T \le 10^3) — the number of test cases.
Each test case consists of a single line containing three integers S, A, and B (-10^{15} \le S \le 10^{15}; 0 \le A \le B \le 10^9).
Output
For each test case, if a solution exists, print YES followed by two space-separated integers a_0 and d.
If there are multiple solutions, you can print any of them.
If no solution exists, print NO.
Examples
| standard input | standard output |
|---|
| 1
12 2 4
| YES 1 1
|
| 1
1 0 2
| NO
|