Yet another education system reform has been carried out in Berland recently. The innovations are as follows:

An academic year now consists of *n* days. Each day pupils study exactly one of *m* subjects, besides, each subject is studied for no more than one day. After the lessons of the *i*-th subject pupils get the home task that contains no less than *a*<sub class="lower-index">*i*</sub> and no more than *b*<sub class="lower-index">*i*</sub> exercises. Besides, each subject has a special attribute, the complexity (*c*<sub class="lower-index">*i*</sub>). A school can make its own timetable, considering the following conditions are satisfied:
 -  the timetable should contain the subjects in the order of the complexity's strict increasing; -  each day, except for the first one, the task should contain either *k* times more exercises, or more by *k* compared to the previous day (more formally: let's call the number of home task exercises in the *i*-th day as *x*<sub class="lower-index">*i*</sub>, then for each *i* (1 &lt; *i* ≤ *n*): either *x*<sub class="lower-index">*i*</sub> = *k* + *x*<sub class="lower-index">*i* - 1</sub> or *x*<sub class="lower-index">*i*</sub> = *k*·*x*<sub class="lower-index">*i* - 1</sub> must be true); -  the total number of exercises in all home tasks should be maximal possible. 
All limitations are separately set for each school.

It turned out that in many cases *a*<sub class="lower-index">*i*</sub> and *b*<sub class="lower-index">*i*</sub> reach 10<sup class="upper-index">16</sup> (however, as the Berland Minister of Education is famous for his love to half-measures, the value of *b*<sub class="lower-index">*i*</sub> - *a*<sub class="lower-index">*i*</sub> doesn't exceed 100). That also happened in the Berland School №256. Nevertheless, you as the school's principal still have to work out the timetable for the next academic year...
The first line contains three integers *n*, *m*, *k* (1 ≤ *n* ≤ *m* ≤ 50, 1 ≤ *k* ≤ 100) which represent the number of days in an academic year, the number of subjects and the *k* parameter correspondingly. Each of the following *m* lines contains the description of a subject as three integers *a*<sub class="lower-index">*i*</sub>, *b*<sub class="lower-index">*i*</sub>, *c*<sub class="lower-index">*i*</sub> (1 ≤ *a*<sub class="lower-index">*i*</sub> ≤ *b*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">16</sup>, *b*<sub class="lower-index">*i*</sub> - *a*<sub class="lower-index">*i*</sub> ≤ 100, 1 ≤ *c*<sub class="lower-index">*i*</sub> ≤ 100) — two limitations to the number of exercises on the *i*-th subject and the complexity of the *i*-th subject, correspondingly. Distinct subjects can have the same complexity. The subjects are numbered with integers from 1 to *m*. 

Please do not use the %lld specificator to read or write 64-bit numbers in С++. It is preferred to use the cin stream or the %I64d specificator.
print("_RANDOM_GUESS_1692167036.125987")# 1692167036.1260037