Integral Pyramid

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.