Education Reform

1000ms

262144K

Description:

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 10¹⁶ (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...

Input:

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 ≤ 10¹⁶, 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.

Output:

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.

Sample Input:

Sample Output:

Sample Input:

Sample Output:

NO

Informação

Provedor Codeforces

Código CF119C