[SCOI2016] 幸运数字

#include<bits/stdc++.h>
#define maxn 20005
#define maxm 65
#define inf 0x7fffffff
#define ll long long
#define rint register ll
#define debug(x) cerr<<#x<<": "<<x<<endl
#define fgx cerr<<"--------------"<<endl
#define dgx cerr<<"=============="<<endl

using namespace std;
ll n,m=61,q,hd[maxn],to[maxn<<1],nxt[maxn<<1];
ll G[maxn],tp[maxn],cnt;
struct basis{
    ll b[maxm];
    inline void clear(){memset(b,0,sizeof(b));}
    inline void ins(ll x){for(rint i=m-1;i>=0;i--)if((x>>i)&1){if(b[i])x^=b[i];else{b[i]=x;break;}}}
};

inline ll read(){
    ll x=0,f=1; char c=getchar();
    for(;!isdigit(c);c=getchar()) if(c==‘-‘) f=-1;
    for(;isdigit(c);c=getchar()) x=x*10+c-‘0‘;
    return x*f;
}

inline void addedge(ll u,ll v){
    to[++cnt]=v,nxt[cnt]=hd[u],hd[u]=cnt;
    to[++cnt]=u,nxt[cnt]=hd[v],hd[v]=cnt;
}

inline basis merge(basis x,basis y){
    basis res; res=x;
    for(rint i=0;i<m;i++) 
        if(y.b[i]) res.ins(y.b[i]);
    return res; 
}

struct Segmentree{
    ll dep[maxn],top[maxn],siz[maxn],son[maxn];
    ll fa[maxn],id[maxn],rk[maxn]; 
    basis tr[maxn<<2];
    inline void dfs1(ll u,ll f){
        fa[u]=f,dep[u]=dep[f]+1,siz[u]=1;
        for(rint i=hd[u];i;i=nxt[i]){
            ll v=to[i]; if(v==f) continue;
            dfs1(v,u),siz[u]+=siz[v];
            if(siz[v]>siz[son[u]]) son[u]=v;
        }
    }
    inline void dfs2(ll u,ll t){
        top[u]=t,id[++id[0]]=u,rk[u]=id[0];
        if(son[u]) dfs2(son[u],t);
        for(rint i=hd[u];i;i=nxt[i])
            {ll v=to[i];if(v!=fa[u]&&v!=son[u])dfs2(v,v);}
    }
    inline void build(ll l,ll r,ll k){
        if(l==r){tr[k].ins(G[id[l]]);return;}
        ll mid=l+r>>1;
        build(l,mid,k<<1),build(mid+1,r,k<<1|1);
        tr[k]=merge(tr[k<<1],tr[k<<1|1]);
    }
    inline basis qry(ll x,ll y,ll l,ll r,ll k){
        if(x<=l && r<=y) return tr[k];
        ll mid=l+r>>1;
        if(x<=mid && y>mid) return merge(qry(x,y,l,mid,k<<1),qry(x,y,mid+1,r,k<<1|1));
        else if(x<=mid) return qry(x,y,l,mid,k<<1); 
        else return qry(x,y,mid+1,r,k<<1|1);
    }
    inline basis calc(ll u,ll v){
        basis res; res.clear();
        while(top[u]!=top[v]){
            if(dep[top[u]]<dep[top[v]]) swap(u,v);
            res=merge(res,qry(rk[top[u]],rk[u],1,n,1));
            u=fa[top[u]];
        }
        if(dep[u]>dep[v]) swap(u,v);
        res=merge(res,qry(rk[u],rk[v],1,n,1));
        return res;
    }
}Tr;

int main(){
    n=read(),q=read();
    for(rint i=1;i<=n;i++) G[i]=read();
    for(rint i=1;i<n;i++){ll u=read(),v=read();addedge(u,v);}
    Tr.dfs1(1,0),Tr.dfs2(1,1),Tr.build(1,n,1);
    while(q--){
        ll u=read(),v=read(),ans=0;
        basis res=Tr.calc(u,v); 
        for(rint i=m-1;i>=0;i--) 
            if((ans^res.b[i])>ans) ans^=res.b[i];
        printf("%lld\n",ans);
    }
    return 0;
}