CF538G.Berserk Robot

Help! A robot escaped our lab and we need help finding it.

The lab is at the point (0, 0) of the coordinate plane, at time 0 the robot was there. The robot's movements are defined by a program — a string of length l, consisting of characters U, L, D, R. Each second the robot executes the next command in his program: if the current coordinates of the robot are (x, y), then commands U, L, D, R move it to cells (x, y + 1), (x - 1, y), (x, y - 1), (x + 1, y) respectively. The execution of the program started at time 0. The program is looped, i.e. each l seconds of executing the program start again from the first character. Unfortunately, we don't know what program was loaded into the robot when he left the lab.

Our radars managed to find out the position of the robot at n moments of time: we know that at the moment of time t__i the robot is at the point (x__i, y__i). Given this data, either help to determine what program could be loaded into the robot, or determine that no possible program meets the data and the robot must have broken down.

救命！一个机器人逃出了我们的实验室，我们需要帮助找到它。

实验室位于坐标平面的点 $(0, 0)$ 处，时间 $0$ 时机器人位于此处。机器人的运动由一段程序控制——该程序是一个长度为 $l$ 的字符串，仅由字符 U、L、D、R 组成。每秒钟，机器人执行程序中的下一个指令：若机器人当前坐标为 $(x, y)$，则指令 U、L、D、R 分别将其移动至格点 $(x, y + 1)$、$(x - 1, y)$、$(x, y - 1)$、$(x + 1, y)$。程序自时间 $0$ 开始执行，且循环运行，即每经过 $l$ 秒后，程序重新从第一个字符开始执行。不幸的是，我们不知道机器人离开实验室时所加载的程序是什么。

我们的雷达成功探测到了机器人在 $n$ 个时刻的位置：已知在时刻 $t_i$，机器人位于点 $(x_i, y_i)$。根据这些数据，请判断是否存在一个可能的程序满足所有观测结果；若存在，请给出这样一个程序；否则判定不存在满足条件的程序，即机器人必然已发生故障。

The first line of the input contains two space-separated integers n and l (1 ≤ n ≤ 2·105, 1 ≤ l ≤ 2·106).

Next n lines contain three space-separated integers — t__i, x__i, y__i (1 ≤ t__i ≤ 1018,  - 1018 ≤ x__i, y__i ≤ 1018). The radar data is given chronologically, i.e. t__i < t__i + 1 for all i from 1 to n - 1.

输入的第一行包含两个用空格分隔的整数 $n$ 和 $l$（$1 ≤ n ≤ 2·10^5$，$1 ≤ l ≤ 2·10^6$）。

接下来的 $n$ 行每行包含三个用空格分隔的整数：$t_i$、$x_i$、$y_i$（$1 ≤ t_i ≤ 10^{18}$，$-10^{18} ≤ x_i, y_i ≤ 10^{18}$）。雷达数据按时间顺序给出，即对所有 $i$（从 $1$ 到 $n-1$），均有 $t_i < t_{i+1}$。

Print any of the possible programs that meet the data. If no program meets the data, print a single word 'NO' (without the quotes).

输出任意一个满足数据的程序。如果不存在满足数据的程序，则输出单个单词 “NO”（不含引号）。