Running with Obstacles

题意翻译

一场跑步比赛在一条数轴上进行，从原点开始向右奔跑。赛程的长度为m，其中有n个位置不同障碍，分布在x1,x2…xn处。运动员在连续跑步至少s个单位（并且不碰到障碍）以后可以跳起越过障碍，但跳跃距离不能超过d个单位。求一种可以完成比赛的移动序列。 Translated by @vanilla

题目描述

A sportsman starts from point $ x_{start}=0 $ and runs to point with coordinate $ x_{finish}=m $ (on a straight line). Also, the sportsman can jump — to jump, he should first take a run of length of not less than $ s $ meters (in this case for these $ s $ meters his path should have no obstacles), and after that he can jump over a length of not more than $ d $ meters. Running and jumping is permitted only in the direction from left to right. He can start andfinish a jump only at the points with integer coordinates in which there are no obstacles. To overcome some obstacle, it is necessary to land at a point which is strictly to the right of this obstacle. On the way of an athlete are $ n $ obstacles at coordinates $ x_{1},x_{2},...,x_{n} $ . He cannot go over the obstacles, he can only jump over them. Your task is to determine whether the athlete will be able to get to the finish point.

输入输出格式

输入格式

The first line of the input containsd four integers $ n $ , $ m $ , $ s $ and $ d $ ( $ 1<=n<=200000 $ , $ 2<=m<=10^{9} $ , $ 1<=s,d<=10^{9} $ ) — the number of obstacles on the runner's way, the coordinate of the finishing point, the length of running before the jump and the maximum length of the jump, correspondingly. The second line contains a sequence of $ n $ integers $ a_{1},a_{2},...,a_{n} $ ( $ 1<=a_{i}<=m-1 $ ) — the coordinates of the obstacles. It is guaranteed that the starting and finishing point have no obstacles, also no point can have more than one obstacle, The coordinates of the obstacles are given in an arbitrary order.

输出格式

If the runner cannot reach the finishing point, print in the first line of the output "IMPOSSIBLE" (without the quotes). If the athlete can get from start to finish, print any way to do this in the following format: - print a line of form "RUN X>" (where "X" should be a positive integer), if the athlete should run for "X" more meters; - print a line of form "JUMP Y" (where "Y" should be a positive integer), if the sportsman starts a jump and should remain in air for "Y" more meters. All commands "RUN" and "JUMP" should strictly alternate, starting with "RUN", besides, they should be printed chronologically. It is not allowed to jump over the finishing point but it is allowed to land there after a jump. The athlete should stop as soon as he reaches finish.

输入输出样例

输入样例 #1

3 10 1 3
3 4 7

输出样例 #1

RUN 2
JUMP 3
RUN 1
JUMP 2
RUN 2

输入样例 #2

2 9 2 3
6 4

输出样例 #2

IMPOSSIBLE