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E - Patisserie ABC 2

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.

2 5

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.

1000000 1000000000000000000

1000000 1000000 1000000

The values in input may be large.

9 47

3 1 4