# Planete

The European Space Agency has $N$ telescopes observing distant
planets. They have classified $M$ different types of events. They
noticed that every day on each planet there is **exactly one** type of event. They measure events
in days because they discovered each event lasts at least one
day, and at most 365 days. Events last only complete numbers of
days, they never last a fractional part of a day. Each event of
the same type lasts exactly the same number of days every time
it occurs, **regardless of the planet it
occurs on**.

After many years of observation they want to analyze data. The telescopes logged all observations, but unfortunately they forgot to write down the year the observations took place! Each telescope entry consists of start date, end date and the number of events observed of each type. Given all observations on all the planets, calculate the duration of each type of event. Note that the telescopes are super precise and start working exactly when the event starts and end when an event ends, not necessarily the same one.

**Note: for this task, each year has
exactly 365 days.**

## Input

The first line contains $N$ and $M$ ($1 \le N, M \le 200$) - the number of telescopes and the number of event types. The next $N$ lines each contains $M + 4$ numbers each:

$D_1\text { }M_1\text { }D_2\text { }M_2\text { }F_1\text { }F_2\text { }...\text { }F_ M$

where $D_1, M_1$ ($01 \le D \le 31, 01 \le M \le 12$) is the start date, $D_2, M_2$ is the end date and $F_ i$ ($0 \le F_ i \le 200$) is the number of times event $I$ was observed.

Note that the days $D_ i$ and months $M_ i$ will always be zero-padded to exactly 2 characters.

## Output

One line containing $M$
numbers, the durations of the event types. If more than one
solution exists, output any one. If no solution exists, output
`“-1”` (without quotes).

Sample Input 1 | Sample Output 1 |
---|---|

1 1 26 02 03 03 1 |
5 |

Sample Input 2 | Sample Output 2 |
---|---|

1 1 26 02 03 03 2 |
185 |

Sample Input 3 | Sample Output 3 |
---|---|

3 3 22 03 01 10 9 10 10 05 05 16 12 1 7 10 20 06 15 01 4 9 10 |
102 204 125 |