Polynomial interpolation

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Problem

Polynomial sequence and interpolation (n<=4)
--nfouille

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Sample input:_

1
0 1
0.5 0.5
0 0.25 0.5 0.25
1 1
1 2 3
-1 2 -3 4

Sample output:

1 2 3 4 5 6 7 8 9
1 4 9 16 25 36 49 64 81
1 3 6 10 15 21 28 36 45
1 9 36 100 225 441 784 1296 2025
2 6 12 20 30 42 56 72 90
6 34 102 228 430 726 1134 1672 2358
2 46 258 860 2170 4602 8666 14968 24210

Sample input:_

1 2 3 4 5 6 7 8 9
1 4 9 16 25 36 49 64 81
1 3 6 10 15 21 28 36 45
1 9 36 100 225 441 784 1296 2025
2 6 12 20 30 42 56 72 90
6 34 102 228 430 726 1134 1672 2358
2 46 258 860 2170 4602 8666 14968 24210

Sample output:

1
0 1
0.5 0.5
0 0.25 0.5 0.25
1 1
1 2 3
-1 2 -3 4

Sample input:_

1 1 2
6 30 84 180 330 546 840 1224 1710
0 0 1
3 16 45 96 175 288 441 640 891

Sample output:

4 22 66 148 280 474 742 1096 1548
1 3 2
1 8 27 64 125 216 343 512 729
0 2 1

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