Given two numbers \(A = (A_0A_1...A_n)\) and \(B = (B_0B_1..B_n)\) in base \(10\), we define the xor of A and B as \(A \odot B = (X_0X_1...X_n)\), where \(X_i = (A_i + B_i) \mod 10\).

Little Achraf has an array S of integers in base \(10\) and he was asked by his professor Toman to find the maximum number he can get by xoring exactly k numbers.

Input format:

First line contains two integers n and k, denoting the number elements in the sequence, and the number of integers you have to xor. Next line contains n integers.

Output format:

Output a single integer denoting the answer of the problem in base \(10\).

Constraints:

\(1 \le n \le 40\)
\(1 \le k \le n\)
\(0 \le S_i \le 10^9\), for all \(i \in [1, n]\)