You're looking at a sort of clock which has a row of N lights. Each light is either on or off, and their states can be read as an N-digit binary number. The first light represents the most significant (leftmost) digit while the Nth light represents the least significant digit. A light that's on corresponds to a 1, and a light that's off corresponds to a 0.
You've just started looking at the clock, and you know that every second from now on, it will count upwards by 1, with its lights turning on or off to display the next number in binary. Once the clock displays 2N - 1 (with all N lights on), it will wrap around to display 0 (with all lights off) on the following second, and then continue counting up again.
However, 0 or more of the clock's lights may be permanently broken. You don't know which ones those are, but you know that they'll always appear to be off, even when they should be on.
Currently, the _i_th light appears to be on if Li = 1, and otherwise appears to be off (if Li = 0). You have also received insider information that exactly K of the lights are currently supposed to be on. It's guaranteed that K is at least as large as the number of lights which appear to be on.
Assuming you stand around and look at this clock for a while, what's the maximum amount of time you might have to wait before you can be completely sure of what state every single light is currently supposed to be in? It's possible that you can be sure immediately, after 0 seconds. On the other hand, it's also possible that you might never be sure, no matter how long you wait.
Input
Input begins with an integer T, the number of different clocks you own. For each clock, there is first a line containing the two space-separated integers, N and K. Then there is a line containing N space- separated integers, the _i_th of which is Li.
Output
For the _i_th clock, print a line containing "Case #i: " followed by the maximum number of seconds which might go by before you know the true current state of each light, or -1 if you might never know.
Constraints
1 ≤ T ≤ 5,000
1 ≤ N ≤ 60
0 ≤ K ≤ N
0 ≤ Li ≤ 1
Explanation of Sample
In the first case, exactly one of the two rightmost lights is initially supposed to be on, so the clock is either supposed to be showing 101 (5) or 110 (6). After one second, the clock will be supposed to show either 110 (6) or 111 (7). Supposing that the two rightmost lights are both broken, both of these values will still look like 100 to you, so you won't be able to tell which one is correct. After one more second, the clock will be supposed to show either 111 (7) or 000 (0). At that point, by observing the functioning leftmost light, you can determine whether all three lights are supposed to be on or off at that moment.
In the second case, you'll never be able to tell which of the two leftmost lights are supposed to be on if they're both broken.