Mo loves finding patterns in numbers. For example, in the sequence $1, 4, 7, (\dots)$, the difference between adjacent numbers is $3$, so the number in the parentheses should be $10$. In another example, $3, 6, 12, (\dots)$, each number is twice the previous one, so the number in the parentheses should be $24$.

Because she has been playing such games for years, Mo has grown tired of arithmetic and geometric progressions. When she sees the sequence $1, 2, \dots, n$, she wants to change its order as little as possible such that there is no subsequence with a common difference of $A$ or a common ratio of $B$.

Specifically, given integers $n, A, B$, find a permutation $P = (P_1, P_2, \dots, P_n)$ of $1$ to $n$ such that for all $i, j \in \{1, 2, \dots, n\}$, if $i < j$ and $P_i < P_j$, then $P_j \neq P_i + A$ and $P_j \neq P_i \times B$.

The degree $S$ to which the permutation $P$ preserves the original order is defined as: $$S = \sum_{1 \le i < j \le n, P_i < P_j} (P_j - P_i)$$

Your task is to maximize the value of $S$ while satisfying the aforementioned requirements.

Input

The first line contains three positive integers $n, A, B$, as described above. Numbers are separated by a single space.

Output

The first line contains $n$ integers representing the permutation $P$ you found, with numbers separated by spaces.

Examples

Input 1

4 3 2

Output 1

4 2 1 3

Note

For this permutation, $S = 3$, which is the maximum possible value for $n = 4, A = 3, B = 2$.

Subtasks

Each test case is scored individually.

For each test case, if your output is invalid (e.g., incorrect file format, the solution does not meet the requirements), you will receive $0$ points. Otherwise, let $your\_ans$ be the $S$ value of your permutation and $our\_ans$ be the $S$ value of the permutation provided by us. Your score for the test case is calculated as follows:

If $your\_ans \ge our\_ans$, you receive $10$ points. Otherwise, your score is: $\max \left\{ \lfloor 10 \times e^{\frac{your\_ans}{our\_ans} - 2} \rfloor, 1 \right\}$.

Constraints

There are a total of $10$ test cases. The data ranges are as follows:

In all input data, $A$ and $B$ are positive integers not exceeding $n$.