//code by Nobody.Emissary
#include<bits/stdc++.h>

#define fi first
#define se second
#define vc vector
#define db double
#define ll long long
#define mk make_pair
#define pb push_back
#define PI pair<int,int>
#define ull unsigned long long
#define err cerr << "   -_-   " << endl
#define debug cerr << " ------------------- " << endl

#define input(x) freopen(#x".in","r",stdin)
#define output(x) freopen(#x".out","w",stdout)

#define NO puts("No")
#define YES puts("Yes")

//#define int long long

using namespace std;

namespace IO{
	inline int read(){
		int X=0, W=0; char ch=getchar();
		while(!isdigit(ch)) W|=ch=='-', ch=getchar();
		while(isdigit(ch)) X=(X<<1)+(X<<3)+(ch^48), ch=getchar();
		return W?-X:X;
	}
	inline void write(ll x){
		if(x<0) x=-x, putchar('-');
		if(x>9) write(x/10);
		putchar(x%10+'0');
	}
	inline void sprint(ll x){write(x), putchar(32);}
	inline void eprint(ll x){write(x), putchar(10);}
}using namespace IO;

const int MAXN = 2e5+5;
const int mod = 998244353;
//const int mod = 1e9+7;

struct op{
	int l, r, add;
};

struct Qask{
	int l, r, id, v;
};

vc<op> Add[MAXN];
vc<Qask> Q[MAXN];

int n, m, id[MAXN], a[MAXN];
int head[MAXN], ne[MAXN<<1], to[MAXN<<1], ecnt;

set<int> S[MAXN];
set<int> :: iterator it;

ll ans[MAXN<<2], tree[MAXN<<2], tag[MAXN<<2], laz[MAXN<<2], cnt[MAXN<<2], sum[MAXN<<2];

inline void add(int x, int y){++ecnt;to[ecnt]=y;ne[ecnt]=head[x];head[x]=ecnt;}

inline void pushup(int p){
	sum[p]=sum[p<<1]+sum[p<<1|1];
	tree[p]=min(tree[p<<1],tree[p<<1|1]);
	cnt[p]=(tree[p]==tree[p<<1])*cnt[p<<1]+(tree[p]==tree[p<<1|1])*cnt[p<<1|1];
	return ;
}

inline void pushdown(int p){
	laz[p<<1]+=laz[p];
	laz[p<<1|1]+=laz[p];
	tree[p<<1]+=laz[p];
	tree[p<<1|1]+=laz[p];
	if(tag[p]){
		if(tree[p<<1]==tree[p]) tag[p<<1]+=tag[p], sum[p<<1]+=1ll*cnt[p<<1]*tag[p];
		if(tree[p<<1|1]==tree[p]) tag[p<<1|1]+=tag[p], sum[p<<1|1]+=1ll*cnt[p<<1|1]*tag[p];
		tag[p]=0; 
	}
	laz[p]=0;
	return ;
}

inline void add(int p, int l, int r, int L, int R, int v){
	if(L>R) return ;
	if(L<=l && r<=R){
		tree[p]+=v; laz[p]+=v;
		return ;
	}
	int mid=(l+r)>>1; pushdown(p);
	if(L<=mid) add(p<<1,l,mid,L,R,v);
	if(R>mid) add(p<<1|1,mid+1,r,L,R,v);
	return pushup(p);
}

inline ll ask(int p, int l, int r, int L, int R){
	if(L<=l && r<=R) return sum[p];
	int mid=(l+r)>>1; ll s=0; pushdown(p);
	if(L<=mid) s+=ask(p<<1,l,mid,L,R);
	if(R>mid) s+=ask(p<<1|1,mid+1,r,L,R);
	return s; 
}

inline void build(int p, int l, int r){
	if(l==r) return tree[p]=0, cnt[p]=1, void();
	int mid=(l+r)>>1;
	build(p<<1,l,mid); build(p<<1|1,mid+1,r);
	return pushup(p);
}

inline void dfs(int x){
	int val=a[x]; vc<int> son; int cur, t, v;
	for(int i=head[x];i;i=ne[i]) dfs(to[i]), son.pb(to[i]);
	if(son.size()==0) return ;
	cur=id[son.back()]; son.pop_back();
	for(auto i:son){
		t=id[i];
		if(S[cur].size()<S[t].size()) swap(cur,t);
		for(auto j:S[t]){
			it=S[cur].lower_bound(j);
			if(it!=S[cur].end()){
				v=*it;
				if(j>val) Add[val+1].pb(op{v,n,1}), Add[j+1].pb(op{v,n,-1});
				else{
					if(v<val) Add[1].pb(op{v,val-1,1}), Add[j+1].pb(op{v,val-1,-1});
				}
			}
			if(it!=S[cur].begin()){
				--it;
				v=*it;
				if(j>val){
					if(v>val) Add[val+1].pb(op{j,n,1}), Add[v+1].pb(op{j,n,-1});
				}
				else Add[1].pb(op{j,val-1,1}), Add[v+1].pb(op{j,val-1,-1});
			}
		}
		for(auto j:S[t]) S[cur].insert(j);
		S[t].clear(); 
	}
	S[cur].insert(a[x]); id[x]=cur;
	return ;
}

signed main(){
	n=read(), m=read(); int f;
	for(int i=1;i<=n;++i) a[i]=read();
	for(int i=2;i<=n;++i) f=read(), add(f,i);
	for(int i=1;i<=n;++i) id[i]=i, S[i].insert(a[i]); dfs(1);
	for(int i=1;i<=m;++i){
		int l, r;
		l=read(), r=read();
		Q[l-1].pb(Qask{l,r,i,-1});
		Q[r].pb(Qask{l,r,i,1});
	}
	build(1,1,n);
	for(int i=2;i<=n;++i) Add[i].pb(op{i-1,i-1,1});
	for(int i=1;i<=n;++i){
		for(auto j:Add[i]) add(1,1,n,j.l,j.r,j.add);
		if(tree[1]==0) tag[1]++, sum[1]+=cnt[1];
		for(auto j:Q[i]) ans[j.id]+=j.v*ask(1,1,n,j.l,j.r);
	}
	for(int i=1;i<=m;++i) eprint(ans[i]);
	return 0;
}