Larry is collecting buckets of water. He has () buckets in a line, each starting empty and having a capacity of (). Every once in a while, someone comes to pour some water in a continuous segment of buckets, pouring the same amount of water in each bucket.

Larry wants to know when each bucket will overflow.

#### Input Specification

The first line of input will consist of three integers: and , indicating that pours happpened.

The next lines of input will each consist of three integers, , and , indicating someone poured water into buckets in segment .

#### Output Specification

The output should consist of space separated integers, the th integer indicating that the th bucket was filled after the th pour (starting at 1).

If a bucket is never filled, output instead.

#### Subtasks

##### Subtask 1 (10%)

##### Subtask 2 (90%)

No further constraints.

#### Sample Input

```
3 3 1
1 2 3
```

#### Sample Output

`1 1 -1`

## Comments