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Background

我出的都是水题。。

Description

Qiyueliuhuo get a function \(f(x)\)，he wants to know what \(f(x)\) is.

Now what he knows is \(f(x)\) can be written as \(a_0+a_1x^1+a_2x^2+...+a_nx^n\), where \(a_0,a_1,...a_n \in \{0,1,2,3...\}\). Also he knows the value of \(f(0),f(2)....f(k)\)。

He needs help.

Format

Input

\(k+2\) integers \(k,f(0),f(2)...f(k)\), satisfying \( k>15\),\(length(f(k))<100\).

Output

\(n+1\) integer in a single line, from \(a_0\) to \(a_n\), \(a_n \neq 0\), satisfy \(15 \geq \sum a_i \)

Sample 1

Input

16
5
15
25
35
45
55
65
75
85
95
105
115
125
135
145
155
165

Output

5 10

Limitation

1s, 1024*256KiB for each test case.

Source

Vijos Original