Festival Wristband Quorum Code

At WaveForm Fest, every attendee wristband is stamped with an access code: a non-negative integer whose bits mark which perks (VIP lounge, backstage pass, free parking, and so on) that wristband unlocks. The organizers want a single combo code to hand to the gate staff that captures exactly the perks popular enough to be worth checking for at the gate: a perk bit should be turned on in the combo code precisely when at least k of the n issued wristbands have that bit turned on. Given the n wristband codes and the threshold k, compute the combo code.

Input format

• Line 1: two integers n and k separated by a space.
• Line 2: n integers code[1] ... code[n] separated by spaces — the wristband access codes.

Output format

Print a single integer: the combo code, i.e. the non-negative integer whose bit b is set (for every 0 <= b <= 30) exactly when at least k of the n wristband codes have bit b set.

Constraints

• 1 <= n <= 50
• 1 <= k <= n
• 0 <= code[i] < 2^31 for every i

3 2
7 12 9

13

3 3
5 5 5

5