A Prime Matrix is defined as an $n \times n$ square matrix satisfying:
All numbers in the matrix are positive integers, and
The numbers in each row are distinct, and
The numbers in each column are distinct, and
The sum of numbers in each row is a prime number, and
The sum of numbers in each column is a prime number.
There may be multiple valid prime matrices out there, but you don’t want the numbers in the matrix to be too large. Given a bound $b$, can you find a prime matrix so that it contains only integers between $1$ and $b$?
The input has a single line with two integers: $n$ ($2 \leq n \leq 50$) and $b$ ($2 \leq b \leq 10^9$).
Output any valid $n \times n$ prime matrix. The output must have $n$ rows. Each row must have $n$ space-separated integers between $1$ and $b$ without leading zeroes. If no such matrix exists, output “impossible”.
Sample Input 1 | Sample Output 1 |
---|---|
3 9 |
1 2 8 7 1 3 3 4 6 |
Sample Input 2 | Sample Output 2 |
---|---|
3 3 |
impossible |