Sum of Dice

By Deyao Chen

Problem Statement

You throw a special programmers' die, which has $6$ faces with $0$, $1$, $2$, $3$, $4$, or $5$ dots, $n$ times. In how many different ways can the sum of all the throws be $s$, for all $s$ from $0$ to $k - 1$? Since the answer can be astronomically large, output the remainder of each number divided by $7340033$.

Constraints

$1 \le n \le 10^{5}$ and $1 \le k \le 10^{4}$

Subtask 1 (10%)

$1 \le n \le 9$

Subtask 2 (10%)

$k - n \le 5$

Subtask 3 (20%)

$1 \le n \le 10$ and $1 \le k \le 300$

Subtask 4 (10%)

$1 \le k \le 300$

Subtask 5 (50%)

No more constraints.

Input

Input consists of a line containing $n$ and $k$, separated by a space.

Output

Output a list of numbers, separated by a space which is the different ways in which the sum of all the throws become $0, 1, 2, 3, ..., \text{or}, k-1$, respectively.

Examples

1 10

1 1 1 1 1 1 0 0 0 0

3 17

1 3 6 10 15 21 25 27 27 25 21 15 10 6 3 1 0