In the "XCPC" competition series, there are four types of medals: gold, silver, bronze, and iron, with values of $4, 3, 2, 1$ respectively. In this problem, $2$ iron medals can be combined into $1$ bronze medal, $2$ bronze medals can be combined into $1$ silver medal, and $2$ silver medals can be combined into $1$ gold medal.

You currently have $n$ iron medals. You can perform combinations to change the number of medals you possess. Let the quadruple $(a_1, a_2, a_3, a_4)$ represent the number of gold, silver, bronze, and iron medals, respectively.

Please answer $n$ questions, where the $i$-th question ($1 \le i \le n$) is: * Given that you start with exactly $n$ iron medals, how many distinct quadruples $(a_1, a_2, a_3, a_4)$ are possible such that: (1) the total number of medals is $i$, i.e., $a_1 + a_2 + a_3 + a_4 = i$; (2) the total value of the medals is at least $p$, i.e., $4a_1 + 3a_2 + 2a_3 + a_4 \ge p$. Here, $p$ is given as input.

Two quadruples are considered different if and only if they differ in at least one corresponding position.

Input

The first line contains two integers $n, p$ ($1 \le p \le n \le 10^6$), separated by a space, representing the initial number of iron medals and the required total medal value $p$, respectively.

Output

Output a single line containing $n$ integers, separated by spaces, where the $i$-th integer ($1 \le i \le n$) represents the answer to the $i$-th question.

Examples

Input 1

8 7

Output 1

0 0 1 2 2 1 1 1

Input 2

10 8

Output 2

0 0 1 2 2 2 2 1 1 1

Input 3

12 1

Output 3

0 1 2 2 3 3 2 2 2 1 1 1