// Starcraft 2 enjoyer //
#include <bits/stdc++.h>
using namespace std;
#define LSOne(X) ((X) & -(X))
const int N = 2e5 + 5;
const int M = 1e7 + 5;
const int LG = 31;
const int C = 26;
const int INF = 1e9 + 5;
struct PersistentSegmentTree
{
struct Node
{
int val;
Node *le, *ri;
Node(Node *a, Node *b)
{
val = a->val + b->val;
le = a;
ri = b;
}
Node(Node *a)
{
val = a->val;
le = a->le;
ri = a->ri;
}
Node(int i)
{
val = i;
le = ri = NULL;
}
} *root[N];
int n, cid;
Node *build(int l, int r)
{
if (l == r)
{
return new Node(1LL);
}
else
{
int m = (l + r) / 2;
return new Node(build(l, m), build(m + 1, r));
}
}
Node *update(Node *cur, int v, int p, int l, int r)
{
if (l == r)
{
return new Node(v);
}
else
{
int m = (l + r) / 2;
if (p <= m)
{
return new Node(update(cur->le, v, p, l, m), cur->ri);
}
else
{
return new Node(cur->le, update(cur->ri, v, p, m + 1, r));
}
}
}
int get(Node *cur, int l, int r, int tl, int tr)
{
if (tl > tr)
return 0;
if (tl <= l && r <= tr)
{
return cur->val;
}
else
{
int m = (l + r) / 2;
return get(cur->le, l, m, tl, min(tr, m)) + get(cur->ri, m + 1, r, max(tl, m + 1), tr);
}
}
void build(int len)
{
n = len;
root[0] = build(0, n - 1);
cid = 1;
}
void update(int v, int p, int i)
{
root[i] = update(root[i], v, p, 0, n - 1);
}
int get(int l, int r, int i)
{
if (l > r)
swap(l, r);
return get(root[i], 0, n - 1, l, r);
}
void add(int i)
{
root[cid++] = new Node(root[i]);
}
};
int n, q;
vector<int> val[N];
void solve()
{
cin >> n >> q;
for (int x = 0; x < n; x++)
{
int i;
cin >> i;
val[i].push_back(x);
}
PersistentSegmentTree pst;
pst.build(n);
for (int x = 1; x < N; x++)
{
pst.add(x - 1);
for (int i : val[x - 1])
{
pst.update(0, i, x);
}
}
for (int x = 0; x < q; x++)
{
int l, r;
cin >> l >> r;
l--;
r--;
int le = 0, ri = n, ans = 0;
while (le <= ri)
{
int m = (le + ri) / 2;
if (pst.get(l, r, m) >= m)
{
ans = m;
le = m + 1;
}
else
{
ri = m - 1;
}
}
cout << ans << "\n";
}
}
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int t = 1;
// cin >> t;
for (int x = 1; x <= t; x++)
{
solve();
}
return 0;
}
