6705: ABC200 —— E - Patisserie ABC 2
[Creator : ]
Description
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:
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.
Input
Input is given from Standard Input in the following format:
$N\ K$
$N\ K$
Output
Print three integers representing the cake's beauty, taste, popularity, in this order, with spaces in between.
Constraints
All values in input are integers.
$1 \le N \le 10^6$
$1 \le K \le N^3$
$1 \le N \le 10^6$
$1 \le K \le N^3$
Sample 1 Input
2 5
Sample 1 Output
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.
$(1,1,1),(1,1,2),(1,2,1),(2,1,1),(1,2,2),(2,1,2),(2,2,1),(2,2,2)$.
Here, each triple of integers represents the beauty, taste, and popularity of a cake.
Sample 2 Input
1000000 1000000000000000000
Sample 2 Output
1000000 1000000 1000000
Sample 3 Input
9 47
Sample 3 Output
3 1 4