The Czechoslovak Legion decided to stop the fierce fighting in Siberia
and return home. However, it was not so easy to leave Russia, because
they had too little money to pay for the sea voyage from Vladivostok to Europe.
The Czechs decided to get the necessary amount of money by
selling their rifles to the advancing Red troops. The total number of rifles
they could sell was n. The first two rifles were ordinary, so the Czechs
asked only one rouble for each of them. The ith rifle (i ≥ 3) costs
as much as the (i−1)th and (i−2)th rifles together.
The bank notes that circulated in Russia at that time had nominal values
equal to powers of an integer k (there were onerouble, krouble,
k^{2}rouble notes and so on). The Red troops had occupied enough printing
plants for printing the necessary amount of notes. They paid for each rifle
the exact amount of money the Czechs asked using the minimal possible
quantity of notes.
When the Red Army got hold of the rifles, Chapaev asked Anka to order them
according to the quantity of notes paid for each rifle. If the same quantity
of notes was paid for two rifles, then the rifle with the smallest number
should go first. Help Anka fulfill this request.
Input
The only line contains the integers k and n separated with a space
(2 ≤ k ≤ 10; 3 ≤ n ≤ 50000).
Output
Output the permutation of the integers from 1 to n corresponding
to the numbers of rifles in the required order.
Sample
input  output 

10 8
 1 2 3 4 8 7 5 6

Notes
After Anka fulfills Chapaev's request, the costs of the rifles in roubles
will be {1, 1, 2, 3, 21, 13, 5, 8}.
Problem Author: Viktor Kamashev
Problem Source: NEERC 2010, Eastern subregional contest