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문제

Pascal’s triangle is a marvel of the combinatorical world, and what’s more you can easily build one for yourself at home.

The lowest row has n numbers. The next row is staggered and has n − 1 numbers, where the ith is the sum of the ith and the i + 1th on the previous row.

You can choose any positive integers for the lowest row, but the single cell on the top row needs to be equal to a given x. Is this possible?

입력

  • The only line contains the number of rows, n (1 ≤ n ≤ 20), and the value needed at the top, x (1 ≤ x ≤ 109).

출력

If a pyramid can be constructed, output all of the numbers on each row, starting from the top. Every number must be greater than or equal to 1.

Otherwise, output impossible.

예제 입력 1

3 15

예제 출력 1

15
8 7
3 5 2

예제 입력 2

6 789

예제 출력 2

789
394 395
209 185 210
117 92 93 117
70 47 45 48 69
45 25 22 23 25 44

예제 입력 3

20 1

예제 출력 3

impossible