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