4. Sum
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Given a natural number $$$S$$$, determine whether it is possible to represent $$$S$$$ as a sum of consecutive integers, where the number of terms is between $$$A$$$ and $$$B$$$ (inclusive).

Input

Three integers — $$$S$$$, $$$A$$$, and $$$B$$$ are provided, each on a separate line ($$$1 \le S \le 2 \cdot 10^9$$$, $$$1 \le A \le B \le 10^6$$$).

Output

If a solution exists, output two integers: the first term of the sequence and the total number of terms. If multiple solutions exist, output the one where the first term is as large as possible. If no solution exists, output «NO» (without quotation marks, both letters capitalized).

Scoring

Subtask 1 (up to 30 points): $$$S \le 100$$$, $$$B \le 100$$$

Subtask 2 (up to 30 points): $$$S \le 10^4$$$, $$$B \le 10^5$$$

Subtask 3 (up to 40 points): no additional constraints.

Examples
Input
9
2
5
Output
4 2
Input
5
4
6
Output
-1 5
Input
1
3
4
Output
NO