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Inspired by the Ulam spiral, which unravels strange patterns of prime numbers' distribution, Petya decided to come up with his own analog.
Petya writes down integers from $1$ to $n^2$ into square table of size $n\times n$ starting from the upper left corner. Numbers from $1$ to $n$ go into the first row, numbers from $n + 1$ to $2n$ --- into the second row, and so on.
Then he colors cells which contain the number with no more than $k$ different divisors. After that, Petya studies the resulting picture in hope of finding some patterns. For example, if $n = 7$, $k = 3$, Petya will get the following picture:
Help Petya, print the picture which he will get after coloring, representing colored cells with asterisks <<
*>>, and non-colored cells with dots <<
Input contains two integers $n$ and $k$ ($1 \le n \le 40$, $1 \le k \le n^2$).
Output $n$ lines, each one containing $n$ characters. If the $j$-th cell of $i$-th row of Petya's table is colored, then $j$-th character of $i$-th line should be equal to <<
*>>, and <<
*****.* .*.*.*. ..*.*.. .*.*... *.*.... .*...*. *...*.*