#include <bits/stdc++.h>
using namespace std;
using ll = int;
#define MAXN (200005)
struct node {
ll s,e,m,v;
node *l, *r;
node(ll _s,ll _e){
s = _s;
e = _e;
m = (s + e) >> 1;
v = 0;
if(s != e){
l = new node(s,m);
r = new node(m + 1,e);
}
}
node(node *u){
s = u->s, e = u->e, m = u->m;
v = u->v;
l = u->l, r = u->r;
}
void update(ll x,ll val){
if(s == e){
v += val;
return;
}else{
if(x > m){
r = new node(r);
r -> update(x,val);
}else{
l = new node(l);
l -> update(x,val);
}
v = l->v + r->v;
}
}
ll query(ll x,ll y){
if(s == x && e == y){
return v;
}else{
if(x > m) return r -> query(x,y);
else if(y <= m) return l -> query(x,y);
else return l -> query(x,m) + r -> query(m + 1,y);
}
}
} *root[MAXN];
int main(){
ios_base::sync_with_stdio(false);cin.tie(0);
ll N,Q;
cin>>N>>Q;
ll arr[N];
deque<pair<ll,ll> > p;
for(ll i = 0;i < N;i++){
cin>>arr[i];
p.push_back({arr[i],i});
}
sort(p.begin(),p.end(),greater<pair<ll,ll> >());
root[MAXN - 1] = new node(0,N - 1);
for(ll i = MAXN - 2;i >= 0;i--){
root[i] = new node(root[i + 1]);
while(!p.empty() && p.front().first >= i){
ll val = p.front().first;
ll ind = p.front().second;
root[i] -> update(ind,1);
p.pop_front();
}
}
for(ll q = 0;q < Q;q++){
ll l,r;
cin>>l>>r;
l--;
r--;
ll high = MAXN;
ll low = 0;
while(high - low > 1){
ll mid = (high + low) / 2;
if(root[mid] -> query(l,r) >= mid){
low = mid;
}else{
high = mid;
}
}
cout<<low<<'\n';
}
}
