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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


## 출처

• 문제를 만든 사람: Robin Lee