#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
using namespace std;
typedef long long ll;
const int N = 1e5+5;
int n, q;
int tot, num, f;
int w[N];
int root[N];
int head[N], to[N], nxt[N];
int tre[N*40][2];
int u, x;
vector<int> g[N];
vector<int> id[N];
int ans[N];
void build(int id) {scanf("%d", &w[id]);root[id] = ++tot;int c = tot;for(int i = 30; i >= 0; i--) {if(w[id]&(1<<i)) tre[c][1] = ++tot;else tre[c][0] = ++tot;c = tot;}
}
void update(int u, int v) {if(tre[v][0]>0) {if(tre[u][0]==0) tre[u][0] = tre[v][0];else update(tre[u][0], tre[v][0]);}if(tre[v][1]>0) {if(tre[u][1]==0) tre[u][1] = tre[v][1];else update(tre[u][1], tre[v][1]);}
}
int query(int u, int x) {int res = 0;int c = root[u];for(int i = 30; i >= 0; i--) {int p = (x>>i)&1;if(tre[c][p^1] > 0) res |= (1<<i), c = tre[c][p^1];else if(tre[c][p] > 0) c = tre[c][p];}return res;
}
void dfs(int u) {for(int i = head[u]; ~i; i = nxt[i]) {dfs(to[i]);update(root[u], root[to[i]]);}int len = g[u].size();for(int i = 0; i < len; i++) ans[id[u][i]] = query(u, g[u][i]);
}
int main() {while(~scanf("%d%d", &n, &q)) {tot = num = 0;memset(tre, 0, sizeof(tre));memset(head, -1, sizeof(head));for(int i = 1; i <= n; i++) {g[i].clear();id[i].clear();}for(int i = 1; i <= n; i++) build(i);for(int i = 2; i <= n; i++) {scanf("%d", &f);to[++num] = i; nxt[num] = head[f]; head[f] = num;}for(int i = 1; i <= q; i++) {scanf("%d%d", &u, &x);g[u].push_back(x);id[u].push_back(i);}dfs(1);for(int i = 1; i <= q; i++) printf("%d\n", ans[i]);}
}