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## 1342. Enterprise

Time limit: 2.5 second
Memory limit: 64 MB
To bind a broom it’s a hard work. As there is a very big demand for this high-tech product an brooms binding enterprise is to have a big amount of production workshops. You are to help such an enterprise to allocate the work among the workshops. Each workshop can bind from 0 to K brooms a day. Economists of the enterprise found out that each bound broom has a different prime cost: in most cases the more brooms were bound a day the less prime cost has the last broom bound that day. However, there may be more complicated situations. As a first approximation you may assume every dependence linear. So decided the economists when they determined a dependence of the next in turn broom’s prime cost on the industrial output of the workshop. You are to find out the optimal work load of the workshops.

### Input

The first line contains two integers N and M (1 ≤ NM ≤ 1000) — an amount of workshops and the required industrial output of brooms, respectively.
Then workshops description follows. The (i+1)-st line describes the i-th workshops with three numbers Ki, Pi, and Qi (1 ≤ Ki ≤ 100; 0 ≤ PiQi ≤ 1000) — they are the maximal number of brooms that can be bound at the i-th workshop a day, the prime cost of the first broom and the prime cost of Ki-th broom at the i-th workshop. As it was mentioned above the cost of j-th broom’s production is the linear with respect to j function.

### Output

If the enterprise can’t produce the required number of brooms your program is to output the maximal number of brooms V that can be bound at the enterprise.
Besides, you are to output the total costs on production of M (or V if the enterprise can’t bind M) brooms with optimal allocation of industrial outputs within two digits after a decimal point.
The output format is to be as in sample outputs below.

### Samples

inputoutput
```2 10
6 20 15
100 100 100
```
```Minimum possible cost: 505.00
```
```2 10
5 30 14
1 20 20
```
```Maximum possible amount: 6
Minimum possible cost: 130.00
```
Problem Author: Magaz Asanov and Pavel Egorov
Problem Source: USU Championship 2004