There is a sequence of K N-sided dice. Some of them are fair, while others aren't. More precisely, each die has probability P of being fair and 1 - P of being unfair. A fair die has equal probabilities of rolling each of its N sides. An unfair die can have any probabilities for its sides, generated randomly in the following way:

1. For i from 1 to N, generate a random uniform number from 0 to 1, this is Q_i.
2. The probability of rolling the i-th side is Q_i / (Q_1 + ... + Q_N). Each of the K dice has been rolled M times and we have recorded the outcomes. Your task is to predict, for each die, whether it is fair or unfair based on these outcomes. Your penalty for predicting that a fair die is unfair is X and for the opposite case it is Y. You should try to minimize your total penalty.

Constraints

2 <= N <= 8 15 <= M <= 40 0.5 <= P <= 0.8 0.3 <= X, Y <= 0.7 X + Y = 1 K = 100000

Input

N M P X Y K Count_1_1 ... Count_1_N ... Count_K_1 ... Count_K_N

Output

IsFair_1 ... IsFair_K

Sample input

3 15 0.6 0.35 0.65 3 6 4 5 9 5 1 5 5 5

Sample output

1 0 1

Scoring

All tests are scored independently. Let TP be the total penalty you got on the test. AP = TP / K BAP = Min(P * X, (1 - P) * Y) S = Max((BAP - AP) / BAP, 0) R = S / S_Author

Your result for the test is then:

1. 1.0, if R > 0.999
2. 0.3 + 0.7 * (1 - (1 - (R - 0.8) / 0.2)^0.75), if R > 0.8
3. 0.3 * R / 0.8, otherwise