Problem Description

There are $2m+1$ types of items, with weights $-m,-m+1,\ldots, m-1,m$. There are $a_i$ items of weight $i$.

You need to take some items such that the sum of their weights is exactly $l$. Under this condition, you need to take as many items as possible.

Ask: with the total weight exactly $l$, what is the maximum number of items you can take.

Input Format

The first line contains two numbers $m,l$.

The second line contains $2m+1$ numbers: $a_{-m},a_{-m+1},\ldots, a_{m-1},a_m$.

Output Format

Output one number in a single line, representing the answer. If no solution exists, output impossible.

2 5
2 3 1 1 4

9

3 5
3 1 0 2 0 0 2

impossible

Hint

Subtask $1$ ($5$ points): $m , a_i≤50$.

Subtask $2$ ($15$ points): $m , a_i≤100$.

Subtask $3$ ($20$ points): $m≤30$.

Subtask $4$ ($20$ points): $m ≤50$.

Subtask $5$ ($20$ points): $m ≤ 100$.

Subtask $6$ ($20$ points): no special constraints.

For subtasks $3$ to $6$, if you pass the test points with $\forall i<0,a_i=0$, you can get half of the score.

For all data, $1\leq m \leq 300$, $-10^{18}\le l \le 10^{18}$, $0\le a_i\le 10^{12}$.

Translated by ChatGPT 5