You are given an array $A$ of $n$ elements. Count the number of non-empty unique subsequences of length $k$ of $A$.
_A subsequence of a given sequence is a sequence that can be derived from the given sequence by deleting some or no elements without changing the order of the remaining elements._
### Input
- The first line contains 2 integers $n, k$.
- The second line contains $n$ integers $A_i$.
### Output
- Print the number of unique subsequences, modulo $123456789$.
### Constraints
- $1 \le k \le n \le 2000$.
- $1 \le A_i \le 2000$.
### Example
Input:
```
3 2
1 2 2
```
Output:
```
2
```
