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*_{i} and no more than *b*_{i} exercises. Besides, each subject has a special attribute, the complexity (*c*_{i}). 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*_{i}, then for each*i*(1 <*i*≤*n*): either*x*_{i}=*k*+*x*_{i - 1}or*x*_{i}=*k*·*x*_{i - 1}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*_{i} and *b*_{i} reach 10^{16} (however, as the Berland Minister of Education is famous for his love to half-measures, the value of *b*_{i} - *a*_{i} 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*_{i}, *b*_{i}, *c*_{i} (1 ≤ *a*_{i} ≤ *b*_{i} ≤ 10^{16}, *b*_{i} - *a*_{i} ≤ 100, 1 ≤ *c*_{i} ≤ 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.

If no valid solution exists, print the single word "NO" (without the quotes). Otherwise, the first line should contain the word "YES" (without the quotes) and the next *n* lines should contain any timetable that satisfies all the conditions. The *i* + 1-th line should contain two positive integers: the number of the subject to study on the *i*-th day and the number of home task exercises given for this subject. The timetable should contain exactly *n* subjects.

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