Security System

题目描述

Fox Ciel safely returned to her castle, but there was something wrong with the security system of the castle: sensors attached in the castle were covering her. Ciel is at point $ (1,1) $ of the castle now, and wants to move to point $ (n,n) $ , which is the position of her room. By one step, Ciel can move from point $ (x,y) $ to either $ (x+1,y) $ (rightward) or $ (x,y+1) $ (upward). In her castle, $ c^{2} $ sensors are set at points $ (a+i,b+j) $ (for every integer $ i $ and $ j $ such that: $ 0<=i&lt;c,0<=j&lt;c $ ). Each sensor has a count value and decreases its count value every time Ciel moves. Initially, the count value of each sensor is $ t $ . Every time Ciel moves to point $ (x,y) $ , the count value of a sensor at point $ (u,v) $ decreases by ( $ |u-x|+|v-y| $ ). When the count value of some sensor becomes strictly less than $ 0 $ , the sensor will catch Ciel as a suspicious individual! Determine whether Ciel can move from $ (1,1) $ to $ (n,n) $ without being caught by a sensor, and if it is possible, output her steps. Assume that Ciel can move to every point even if there is a censor on the point.

输入输出格式

输入格式

In the first line there are five integers $ n,t,a,b,c $ ( $ 2<=n<=2·10^{5}, $ $ 0<=t<=10^{14}, $ $ 1<=a<=n-c+1, $ $ 1<=b<=n-c+1, $ $ 1<=c<=n $ ). Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin stream (also you may use the %I64d specificator).

输出格式

If Ciel's objective is possible, output in first line $ 2n-2 $ characters that represent her feasible steps, where $ i $ -th character is R if $ i $ -th step is moving rightward, or U if moving upward. If there are several solution, output lexicographically first one. Character R is lexicographically earlier than the character U. If her objective is impossible, output Impossible.

输入输出样例

输入样例 #1

5 25 2 4 1

输出样例 #1

RRUURURU

输入样例 #2

3 6 1 2 2

输出样例 #2

URUR

输入样例 #3

3 5 1 2 2

输出样例 #3

Impossible

输入样例 #4

20 492 11 4 8

输出样例 #4

RRRRRRRRRRRRRRRRUUUUURUUUUURRUUUUUUUUU

说明

The answers for the first sample and the second sample are shown on the picture:  Here, a red point represents a point that contains a sensor.