codejam2012_1a_a.py

import sys
from pprint import pprint

def solve():
    line1 = [int(x) for x in sys.stdin.readline().strip().split(" ")]

    typed = line1[0]
    total = line1[1]

    probs = [float(x) for x in sys.stdin.readline().strip().split(" ")]
    min_expected = total + 2
    correct_prob = 1.0
    for i in range(typed):
        correct_prob = correct_prob * probs[i]
        chars_keep = i + 1
        keystrokes_if_correct = (typed - chars_keep) + (total - chars_keep) + 1
        keystrokes_if_not_correct = keystrokes_if_correct + total + 1
        expected = keystrokes_if_correct * correct_prob + keystrokes_if_not_correct * (1.0 - correct_prob)
        if expected < min_expected:
            min_expected = expected

    return min_expected

def run():
    cases = int(sys.stdin.readline().strip())
    for i in range(cases):
        print("Case #{}: {}".format(i + 1, solve()))

if __name__ == "__main__":
    run()