Given are a prime number p and a sequence of $p integers a_0, \ldots, a_{p-1}$ consisting of zeros and ones.
Find a polynomial of degree at most $p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \ldots + b_0,$ satisfying the following conditions:
- For each $i (0 \leq i \leq p-1), b_i$ is an integer such that $0 \leq b_i \leq p-1$.
- For each $i (0 \leq i \leq p-1), f(i) \equiv a_i \pmod p$.

-----Constraints-----
- $2 \leq p \leq 2999$
- p is a prime number.
- $0 \leq a_i \leq 1$

-----Input-----
Input is given from Standard Input in the following format:
p
$a_0 a_1 \ldots a_{p-1}$

-----Output-----
Print $b_0, b_1, \ldots, b_{p-1}$ of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.
It can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.

-----Sample Input-----
2
1 0

-----Sample Output-----
1 1

f(x) = x + 1 satisfies the conditions, as follows:
- $f(0) = 0 + 1 = 1 \equiv 1 \pmod 2$
- $f(1) = 1 + 1 = 2 \equiv 0 \pmod 2$

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