Practice Coding with the exercise "Elevator"

Statement

Goal

A building has n floors.
It has an elevator that is controlled by two buttons only: UP and DOWN.

By pressing the UP button, the elevator will go exactly a floors up.
By pressing the DOWN button, the elevator will go exactly b floors down.

If the elevator is commanded to go lower than the first floor or higher than the n-th floor, it will refuse to move and remain on its current floor.

The elevator starts on the k-th floor. Count how many times the buttons should be pressed to move the elevator to the m-th floor.

Input

Line 1: 5 space separated integers in order: n a b k m

Output

One line that contains 1 integer - minimal number of buttons pressed, required to move the elevator to the floor m.

If it is impossible to move the elevator to the floor m, print IMPOSSIBLE

Constraints

1 ≤ n ≤ 10000
1 ≤ a ≤ n
1 ≤ b ≤ n
1 ≤ k ≤ n
1 ≤ m ≤ n

Example

Input

10 1 1 8 5

Output

Solve it

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