1.1 Hill Climb

Score: 30pts

Time Limit: 2.00 sec

A man is driving a car on a sunny afternoon along a slope. There is too much traffic on the road. In one step, the car moves forward n distance, and consequently in the next step, it moves backward m distance, and so on. There is a manhole on the road x distance away from the starting point. How many steps are required before going past the manhole for the first time?

Constraints

1 ≤ x ≤ 10^5

1 ≤ m < n ≤ 5000

1 ≤ m < n ≤ 5000

Input Format

Input consists of a single line containing x, n, m denoting distance of the manhole from start point, forward movement and backward movement respectively.

Output Format

For each test case, output a single line containing the total number of steps.

Example 1

Input:

120 7 4

Output:

77

Explanation:

Net distance in each forward and backward step combined (n-m): 7 - 4 = 3.

After taking 38 forward and 38 backwards steps the man is 114 distance away from where he started. Now, when he takes a forward step of 7 he reaches the distance 121, at which point he has crossed the manhole.

Calculation: (3 * 38 = 114) + 7 = 121 => Total steps: 77

120 7 4

Output:

77

Explanation:

Net distance in each forward and backward step combined (n-m): 7 - 4 = 3.

After taking 38 forward and 38 backwards steps the man is 114 distance away from where he started. Now, when he takes a forward step of 7 he reaches the distance 121, at which point he has crossed the manhole.

Calculation: (3 * 38 = 114) + 7 = 121 => Total steps: 77