Given $n$ objects, where the $i$-th object has a weight of $w_i$. For each weight $k$ from $1$ to $T$, determine whether there is a way to select some objects out of the $n$ objects such that their total weight is $k$.
### Input
- The first line contains two integers $n$ and $T$.
- The second line contains $n$ integers $w_i$.
### Output
- Print a binary string of length $T$, where the $i$-th character is `0` or `1` indicating whether it's impossible or possible to achieve weight $i$.
### Constraints
- $1 \leq n, T, \sum{w_i} \leq 10^6$.
### Example
Input:
```
5 20
4 3 3 4 4
```
Output:
```
00110111011101100100
```
