Garland#876
A garland consists of bulbs on a common wire. One end is fixed at a given height mm (H_1 = A). Due to gravity, the garland bends: the height of each non-terminal bulb is mm less than the average height of its nearest neighbors (H_i = (H_{i-1} + H_{i+1}) / 2 - 1 for 1 < i < N). It is required to find the minimal possible height of the second end (B = H_N), under the condition that no bulb touches the ground (H_i > 0 for 1 \leq i \leq N).
The first line contains two numbers, and . Here 3 \leq N \leq 1000 (integer), 10 \leq A \leq 1000 (real number).
Output a single real number with two digits after the decimal point.
Example 1