#include<algorithm>
#include<cmath>
#include<cstdio>
#include<iostream>
using namespace std;
const int Maxn=1e6+10;
const int Inf=0x3f3f3f3f;
struct node{int val,id;}a[Maxn];
int b[Maxn<<1],c[Maxn];
int ans[Maxn];
int main(){
	ios::sync_with_stdio(false);
	cin.tie(nullptr);cout.tie(nullptr);
	int n,m;cin>>n>>m;m+=n;
	for(int i=1;i<=n;++i)cin>>c[i],a[i]={c[i],i};
	sort(a+1,a+n+1,[](node fi,node se){
		return fi.val>se.val;
	});
	int lim=max(0.,2-7/sqrt(n))*Inf;
	for(int i=1;i<=m;++i){
		cin>>b[i];
		if(i>n)b[i]^=ans[i-1];
		for(int j=1;j<=n;++j){
            if(a[j].val+b[i]<lim)break;
            int k=i-a[j].id+n;
            if(k>=n&&k<=m)
				ans[k]=max(ans[k],a[j].val+b[i]);
        }
        if(i<n)continue;
        if(!ans[i])
            for(int j=1;j<=n;j++)
				ans[i]=max(ans[i],c[j]+b[i-n+j]);
		cout<<ans[i]<<' ';
	}
	return 0;
}