POLEVAL - Evaluate the polynomial

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Your task consists of evaluate a polynomial of degree n (0 <= n <= 999) represented by its n+1 coefficients of the form:

pn(x) = cnxn + cn-1xn-1 + … + c2x2 + c1x + c0

in each one of the k (1 <= k <= 100) points x1, x2, …, xk. The coefficients of the polynomial and the values where they will be evaluated are integers in the interval [-100, 100] that guarantees that the polynomial's evaluation is at the most 263 – 1.

Input

There will be multiple test cases, each one with 4 lines that are described below
n: degree of polynomial.
cn cn-1 … c2 c1 c0: coefficients of the polynomial separated by a single space.
k: number of points to evaluate the polynomial.
x1 x2 xk-1 xk: points to evaluate the polynomial separated by a single space.

The final test case is a single line where n = -1 and this case should not be processed.

Output

For each test case you should print k + 1 lines of output, the very first line containing the case number and the following k lines with the result of the polynomial's evaluation in each one of the k given points. See the sample.

Example

Input:
2
1 -2 -1
5
0 1 -1 2 -2
3
2 1 -2 -1
4
0 -1 2 -2
-1
Output: Case 1:
-1
-2
2
-1
7
Case 2:
-1
0
15
-9

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Alex: 2012-04-13 08:22:43

It's hard not to get TLE in Python


Added by:Ivan Alfonso Olamendy
Date:2007-08-25
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: C99 ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:My own resource