Bimlu loves arrays while his roommate Suyu loves numeric operations on a number. Underestimating their true love towards each other, Guppi wants to check if they actually love each other to that extent by asking them a problem.
Given N integers a1,a2,... an, Bimlu and Suyu have to perform at most k operations. For each operation, they can multiply one of the N numbers by x. Guppi asks them to maximize a1|a2|a3|... an, where | means Bitwise OR.
You need to help Bimlu and Suyu achieve the maximum possible value of a1|a2|a3|... an after performing at most k operations optimally.
INPUT:
The first line contains three integers, N, x, and k. The second line contains N space separated positive integers.
OUTPUT:
Output the maximum value of bitwise OR operation of the N elements after performing the operations.
CONSTRAINTS:
1 ≤ N ≤ 200000
2 ≤ x ≤ 8
1 ≤ k ≤ 10
1 ≤ ai ≤109
EXAMPLES :
Input:
3 2 1
1 1 1
Output:
3
Input:
4 3 2
1 2 4 8
Output:
79
EXPLANATION:
For the first sample, any possible choice of doing one operation will result the same three numbers 1, 1, 2, so the result is 1|1|2 = 3.
For the second sample if we multiply 8 by 3 two times we'll get 72. In this case the numbers will become 1, 2, 4, 72 so the OR value will be 79 and is the largest possible result.