// Judges with GCC >= 12 only needs Ofast
// #pragma GCC optimize("O3,no-stack-protector,fast-math,unroll-loops,tree-vectorize")
// MLE optimization
// #pragma GCC optimize("conserve-stack")
// Old judges
// #pragma GCC target("sse4.2,popcnt,lzcnt,abm,mmx,fma,bmi,bmi2")
// New judges. Test with assert(__builtin_cpu_supports("avx2"));
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma,tune=native")
// Atcoder
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma")
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> ordered_set;
- insert(x),erase(x)
- find_by_order(k): return iterator to the k-th smallest element
- order_of_key(x): the number of elements that are strictly smaller
*/
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,fma")
#include<bits/stdc++.h>
using namespace std;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
uniform_real_distribution<> pp(0.0,1.0);
#define ld long double
#define pii pair<int,int>
#define piii pair<int,pii>
#define mpp make_pair
#define fi first
#define se second
const int mod=998244353;
const int maxn=500005;
const int B=1000;
const int maxs=655;
const int maxm=200005;
const int maxq=1000005;
const int maxl=25;
const int maxa=500000;
const int root=3;
const int base=101;
 
int n,q,a[maxn];
int l[maxn],r[maxn],res[maxn];
vector<int> pos[maxn],qq[maxn];
/*
int bit[maxn];
void update(int x,int val){
    for(int i=x;i<=n;i+=(i&(-i))) bit[i]+=val;
}
int query(int x){
    int ans=0;
    for(int i=x;i>=1;i-=(i&(-i))) ans+=bit[i];
    return ans;
}
*/
int pre[maxn],add[maxn];
int query(int x){
    return pre[x]+add[x/B];
}
void update(int x,int val){
    for(int i=x;i<=n;i++){
        if(i%B==0) add[i/B]+=val,i+=B-1;
        else pre[i]+=val;
    }
}
void solve(){
    cin >> n >> q;
    for(int i=1;i<=n;i++){
        cin >> a[i];
        pos[a[i]].push_back(i);
    }
    for(int i=1;i<=q;i++){
        cin >> l[i] >> r[i];
        qq[r[i]-l[i]].push_back(i);
    }
    for(int i=0;i<=n;i++) for(int x:pos[i]) pre[x]=1;
    for(int i=1;i<=n;i++) pre[i]+=pre[i-1];
    for(int i=n;i>=0;i--){
        for(auto id:qq[i]){
            int total=query(r[id])-query(l[id]-1);
            if(total>i) res[id]=i+1;
            else if(total) qq[total-1].push_back(id);
        }
        for(int x:pos[i]) update(x,-1);
    }
    for(int i=1;i<=q;i++) cout << res[i] << '\n';
}
 
signed main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);cout.tie(NULL);
    int test=1;//cin >> test;
    while(test--) solve();
}

In file included from /usr/include/c++/13/string:43,
                 from /usr/include/c++/13/bitset:52,
                 from /usr/include/x86_64-linux-gnu/c++/13/bits/stdc++.h:52,
                 from answer.code:22:
/usr/include/c++/13/bits/allocator.h: In destructor ‘constexpr std::_Vector_base<int, std::allocator<int> >::_Vector_impl::~_Vector_impl()’:
/usr/include/c++/13/bits/allocator.h:184:7: error: inlining failed in call to ‘always_inline’ ‘constexpr std::allocator< <template-parameter-1-1> >::~allocator() noexcept [with _Tp = int]’: target specific option mismatch
  184 |       ~allocator() _GLIBCXX_NOTHROW { }
      |       ^
In file included from /usr/include/c++/13/vector:66,
                 from /usr/include/c++/13/functional:64,
                 from /usr/include/x86_64-linux-gnu/c++/13/bits/stdc++.h:53:
/usr/include/c++/13/bits/stl_vector.h:133:14: note: called from here
  133 |       struct _Vector_impl
      |              ^~~~~~~~~~~~