fn main() {
    input! {
        n: usize,
        k: usize1,
        a: [u32; n],
    }
    let mut a = a;
    a.sort();
    let ans = dfs(vec![&a], k, 30);
    println!("{}", ans);
}

fn dfs<'a>(a: Vec<&'a [u32]>, k: usize, w: usize) -> u32 {
    if w == 0 {
        return 0;
    }
    let w = w - 1;
    let mut zero = 0;
    let mut p = vec![];
    let mut q = vec![];
    for a in a.iter() {
        let m = a.iter().position(|a| *a >> w & 1 == 1).unwrap_or(a.len());
        let (l, r) = a.split_at(m);
        zero += l.len() * (l.len() - 1) / 2 + r.len() * (r.len() - 1) / 2;
        if l.len() > 0 && r.len() > 0 {
            p.push((l, r));
        }
        if l.len() > 1 {
            q.push(l);
        }
        if r.len() > 1 {
            q.push(r);
        }
    }
    if k >= zero {
        let k = k - zero;
        efs(p, k, w) | (1 << w)
    } else {
        dfs(q, k, w)
    }
}

fn efs<'a>(a: Vec<(&'a [u32], &'a [u32])>, k: usize, w: usize) -> u32 {
    if w == 0 {
        return 0;
    }
    let w = w - 1;
    let mut zero = 0;
    let mut p = vec![];
    let mut q = vec![];
    for (a, b) in a {
        let x = a.iter().position(|a| *a >> w & 1 == 1).unwrap_or(a.len());
        let y = b.iter().position(|a| *a >> w & 1 == 1).unwrap_or(b.len());
        let (al, ar) = a.split_at(x);
        let (bl, br) = b.split_at(y);
        zero += 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 zero <= k {
        efs(q, k - zero, w) | (1 << w)
    } else {
        efs(p, k, w)
    }
}

// ---------- 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 ----------