def parse(inFile):
    [A, B] = inFile.getInts()
    return (A, B, inFile.getFloats())

def solve((A, B, probs)):
    rec = 2 + B
    prob = 1.0
    for i in xrange(A + 1):
        if (i > 0):
            prob = prob * probs[i-1]
        score = (A + B + 1 - (2 * i)) + (1 - prob) * (B + 1)
        if (score < rec):
            rec = score
    return "%.7f" % rec

if __name__ == "__main__":
    from GCJ import GCJ
    GCJ(parse, solve, "/Users/lpebody/gcj/2012_1a/", "a").run()