# 3627. Calculation

You are given an array $A$ with $N$ nodes. The array nodes are numbered from $0$ to $N-1$ (represented by $a_i$).

Then you define a new array $B$. The $i$-th ($0 \le i < N$) node of $B$ is $b_i$:

$$b_i = \sum_{j=0}^{N-1} (a_j (4^i \cdot p + q)^j)) \bmod 200003$$

Please calculate array $B$.

### 输入格式

The first line contains three integers $N$, $p$, $q$ ($1 \le N \le 100000, 1 \le p, q \le 10$).

The next line contains $N$ integers of array $A$. ($0 \le a_i \le 1000$)

### 输出格式

Output $N$ integers of array $B$ in one line separated with space.

### 样例

Input
5 1 1
1 2 3 4 5

Output
129 3711 38153 163078 120839

Input
3 1 2
1 1 1

Output
13 43 343


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