Contest Duration: - (local time) (100 minutes) Back to Home
E - Patisserie ABC 2 /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

「ABC洋菓子店」で働くパティシエである高橋君は、ケーキを作って AtCoder Beginner Contest 200 を祝うことにしました。

その後、高橋君は、できた N^3 個のケーキを以下の順序で並べました。

• 「綺麗さ」+「おいしさ」+「人気度」が小さいものを、より左に並べる。
• ここまでで順序がつかなければ、「綺麗さ」が小さいものを、より左に並べる。
• ここまでで順序がつかなければ、「おいしさ」が小さいものを、より左に並べる。

このとき、左から K 番目にあるケーキの各パラメータの値を求めてください。

制約

• 入力は全て整数
• 1 \le N \le 10^6
• 1 \le K \le N^3

入力

N K


入力例 1

2 5


出力例 1

1 2 2


(1,1,1),(1,1,2),(1,2,1),(2,1,1),(1,2,2),(2,1,2),(2,2,1),(2,2,2)

入力例 2

1000000 1000000000000000000


出力例 2

1000000 1000000 1000000


入力例 3

9 47


出力例 3

3 1 4


Score : 500 points

Problem Statement

Takahashi, a pastry chef at ABC Confiserie, has decided to make cakes to celebrate AtCoder Beginner Contest 200.

A cake made by Takahashi has three parameters: beauty, taste, and popularity, each of which is represented by an integer between 1 and N (inclusive).

He has made a cake of beauty i, taste j, and popularity k for every triple (i,j,k)\ (1 \le i,j,k \le N).
Then, he has arranged these N^3 cakes in a row, as follows:

• The cakes are in ascending order of sum of beauty, taste, and popularity from left to right.
• For two cakes with the same sum of beauty, taste, and popularity, the cake with the smaller beauty is to the left.
• For two cakes with the same sum and the same beauty, the cake with the smaller taste is to the left.

Find the beauty, taste, and popularity of the K-th cake from the left.

Constraints

• All values in input are integers.
• 1 \le N \le 10^6
• 1 \le K \le N^3

Input

Input is given from Standard Input in the following format:

N K


Output

Print three integers representing the cake's beauty, taste, popularity, in this order, with spaces in between.

Sample Input 1

2 5


Sample Output 1

1 2 2


The cakes are in the following order:

(1,1,1),(1,1,2),(1,2,1),(2,1,1),(1,2,2),(2,1,2),(2,2,1),(2,2,2).

Here, each triple of integers represents the beauty, taste, and popularity of a cake.

Sample Input 2

1000000 1000000000000000000


Sample Output 2

1000000 1000000 1000000


The values in input may be large.

Sample Input 3

9 47


Sample Output 3

3 1 4