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.

Input

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).

Output

If Ciel's objective is possible, output in first line $2*n* - 2$ 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.

Note

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.