As a serious strategy-games player, you know how important it is to gather enough food for your army before any invasion. Because of this, you decided to collect at least neededFood units of food for your soldiers.

At the beginning, you have n workers to help you. In a single round, each of your workers gathers one unit of food. At the end of each round, you can trade some of your food for new workers. Hiring a single new worker costs price units of food. You can purchase any amount of new workers as long as you have the food to pay for it.

Find the minimum number of rounds you need to gather at least neededFood units of food.

Input

Each line contains three integers: neededFood, n and price (1 ≤ neededFood, n, price ≤ 1000).

Output

For each test case print in a separate line the minimum number of rounds you need to gather at least neededFood units of food.