Farmer Johns cows are showing off their new dance mooves!

At first, all N cows (2N105,2N105) stand in a line with cow ii in the iith position in line. The sequence of dance mooves is given by K (1K21051K2105) pairs of positions (a1,b1),(a2,b2),,(aK,bK)(a1,b1),(a2,b2),,(aK,bK). In each minute i=1Ki=1K of the dance, the cows in positions ai and bi in line swap. The same K swaps happen again in minutes K+12K K+12K, again in minutes 2K+13K2K+13K, and so on, continuing indefinitely in a cyclic fashion. In other words,

• In minute 1, the cows at positions a1 and b1 swap.
• In minute 2, the cows at positions a2 and b2 swap.
• ...
• In minute K, the cows in positions aK and bK swap.
• In minute K+1, the cows in positions a1 and b1 swap.
• In minute K+2 the cows in positions a2 and b2 swap.
• and so on ...

For each cow, please determine the number of unique positions in the line she will ever occupy.

INPUT FORMAT (input arrives from the terminal / stdin):

The first line contains integers NN and KK. Each of the next KK lines contains (a1,b1)(aK,bK)(a1,b1)(aK,bK) (1ai

OUTPUT FORMAT (print output to the terminal / stdout):

Print NN lines of output, where the iith line contains the number of unique positions that cow ii reaches.