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...

输入描述:

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 ai, bi, ci (1 ≤ ai ≤ bi ≤ 1016, bi - ai ≤ 100, 1 ≤ ci ≤ 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.

输出描述:

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.