Given an array $A$ consisting of $n$ integers, find a way to divide the array into $k$ groups such that each group has the same sum. Each group must contain at least one element.
### Input
- The first line contains two integers $n,k$.
- The second line contains $n$ integers $A_i$.
### Output
- Print $n$ integers, where the $i$-th integer represents the group of the $i$-th element. If there are multiple valid answers, print any of them.
- If there is no solution, print `ze`.
### Constraints
- $2 \le k < n \le 10$.
- $1 \le A_i \le 100$.
### Example
Input:
```
5 3
1 4 6 9 10
```
Output:
```
1 3 3 1 2
```
Explanation:
- The first group consists of two elements $A_2 + A_3 = 4 + 6 = 10$.
- The second group consists of one element $A_5 = 10$.
- The third group consists of two elements $A_1+A_4=1+9=10$.
The answer `1 2 2 1 3` or `3 1 1 3 2` are also acceptable answers.
