fn main() {
    input! {
        n: usize,
        k: usize1,
        a: [u32; n],
    }
    let mut a = a;
    a.sort();
    let mut a = vec![(a.as_slice(), a.as_slice())];
    let mut k = 2 * k + n;
    let mut ans = 0;
    for i in (0..30).rev() {
        let mut p = vec![];
        let mut q = vec![];
        let mut s = 0;
        for (a, b) in a {
            let x = a.iter().position(|a| *a >> i & 1 == 1).unwrap_or(a.len());
            let y = b.iter().position(|a| *a >> i & 1 == 1).unwrap_or(b.len());
            let (al, ar) = a.split_at(x);
            let (bl, br) = b.split_at(y);
            s += al.len() * bl.len() + ar.len() * br.len();
            p.push((al, bl));
            p.push((ar, br));
            q.push((al, br));
            q.push((ar, bl));
        }
        if s <= k {
            k -= s;
            a = q;
            ans |= 1 << i;
        } else {
            a = p;
        }
        a.retain(|p| p.0.len() > 0 && p.1.len() > 0);
    }
    println!("{}", ans);
}

// ---------- begin input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[macro_export]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[macro_export]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[macro_export]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, bytes) => {
        read_value!($iter, String).bytes().collect::<Vec<u8>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}
// ---------- end input macro ----------