The New Year garland consists of N lamps attached to a common wire that hangs down on the ends to which out- ermost lamps are affixed. The wire sags under the weight of lamp in a particular way: each lamp is hanging at the height that is 1 millimeter lower than the average height of the two adjacent lamps. The leftmost lamp in hanging at the height of A millime- ters above the ground. You have to determine the lowest height B of the rightmost lamp so that no lamp in the gar- land lies on the ground though some of them may touch the ground. You shall neglect the lamp’s size in this problem. By numbering the lamps with integers from 1 to N and denot- ing the i-th lamp height in millimeters as Hi we derive the following equations: • H1 = A • Hi = (Hi−1 + Hi+1)/2 − 1, for all 1 < i < N • HN = B • Hi ≥0,forall1≤i≤N The sample garland with 8 lamps that is shown on the picture has A = 15 and B = 9.75. Input The input file consists of several datasets. Each datasets contains a single line with two numbers N and A separated by a space. N (3 ≤ N ≤ 1000) is an integer representing the number of lamps in the garland, A (10 ≤ A ≤ 1000) is a real number representing the height of the leftmost lamp above the ground in millimeters. Output For each dataset, write to the output file the single real number B accurate to two digits to the right of the decimal point representing the lowest possible height of the rightmost lamp. Sample Input 8 15 692 532.81 Sample Output 9.75 446113.34