P4141 The Missing Item

ftiasch has $n$ items with volumes $w_1,w_2,\dots,w_n$. Due to her negligence, the $i$-th item is missing. “How many ways are there to exactly fill a knapsack of capacity $x$ using the remaining $n-1$ items?” — this is a classic problem. She records the answer as $\text{cnt}(i,x)$ and wants the table of $\text{cnt}(i,x)$ for all $i \in [1,n]$ and $x \in [1,m]$. 

The first line contains two integers $n,m$, the number of items and the maximum capacity. The second line contains $n$ integers $w_1,w_2,\dots,w_n$, the volume of each item.

Output an $n \times m$ matrix, giving the last digit of $\text{cnt}(i,x)$.

Constraints For $100\%$ of the testdata, $1 \le n,m \le 2000$, and $1 \le w_i \le 2000$. Sample explanation If item $3$ is missing, there is exactly one way to fill capacity $2$, namely choosing items $1$ and $2$. — $\text{upd 2023.8.11}$: Added five new hack test sets. Translated by ChatGPT 5