A8105. Security System

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: $0<=i<c,0<=j<c$ ).

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.

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).

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.

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.