Mosquitoes which were brought to Uranus from the Earth, have mutated and
spawned in great amounts. Now Uranians sapiens have to slap themselves
constantly to kill insects that keep trying to suck bioplasm out of them.
This may be the reason why newly gemmated Uranians may have more arms than
their parents. The first offspring of every Uranian has as many arms as
his parent has. The second offspring has twice as many, the third one has
three times as many and so on. None of Uranians can gemmate more than g
children in his life.
Now let's turn to cinema. The first night of the 146th episode of the
Star Wars will take place in g movie halls, and n Uranians are already
queuing for tickets. Cashier Fedya is afraid of brothers starting to sort
things out during the film. That’s why he wants to sell tickets in such a
way that there are no brothers in the same hall. Of course he knows
nothing about their family relationships, but he can see perfectly well
how many arms each Uranian has. Will this information be enough for Fedya to
distribute them into the halls so that there are no Uranians with
a common father in any single hall?
The first line contains integers n and g (1 ≤ n ≤ 50 000;
2 ≤ g ≤ 5). Further there are n different integers, which
specify the number of arms of every Uranian in the queue. Every Uranian
has at least one and at most 109 arms.
If Fedya is able to distribute the Uranians into cinema halls as required,
output “Yes” in the first line, and then output n numbers, showing the
number of the hall for every visitor. The visitors should be described in
the order in which they are given in the input. The halls are
numerated with numbers from 1 to g. If the problem has many solutions you may output any of them.
If there is no solution, output “No”.
Problem Author: Andrey Demidov
Problem Source: Open Ural FU Personal Contest 2012