#include <bits/stdc++.h>
using namespace std;

int inf = 1001001001;

array<int,4> mrg(array<int,4>&a,array<int,4>&b) {
    array<int,4>ar = {0,0,0,0};
    ar[0] = max(a[0],a[2]+b[0]);
    ar[1] = max(b[1],b[2]+a[1]);
    ar[2] = a[2]+b[2];
    ar[3] = max({a[3],b[3],a[1]+b[0]});
    return ar;
}

struct SegmentTree {
    int n;
    vector<array<int,4>> dat;
    SegmentTree() {}
    SegmentTree(int N) {
        n = 1;
        while(n < N) {
            n *= 2;
        }
        dat.resize(2*n-1);
        for(int i = n-1; i < 2*n-1; i++) {
            dat[i] = {1,1,1,1};
        }
        for(int i = n-2; i >= 0; i--) {
            dat[i] = mrg(dat[i*2+1],dat[i*2+2]);
        }
    }
    void update(int x) {
        x += n-1;
        dat[x] = {0,0,-1,0};
        while(x > 0) {
            x = (x-1)/2;
            dat[x] = mrg(dat[2*x+1],dat[2*x+2]);
        }
    }
    array<int,4> query(int a, int b, int k, int l, int r) {
        if(r <= a || b <= l) return {0,0,0,0};
        if(a <= l && r <= b) return dat[k];
        array<int,4> vl = query(a, b, 2*k+1, l, (l+r)/2);
        array<int,4> vr = query(a, b, 2*k+2, (l+r)/2, r);
        return mrg(vl, vr);
    }
    array<int,4> query(int a,int b) {//[a,b)
        return query(a,b,0,0,n);
    }
};

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int N,Q;
    cin >> N >> Q;
    vector<int>A(N);
    for(int i = 0; i < N; i++) {
        cin >> A[i];
    }
    vector<int>L(Q),R(Q);
    for(int i = 0; i < Q; i++) {
        cin >> L[i] >> R[i];
        L[i]--;
        R[i]--;
    }
    vector<int>l(Q,0),r(Q,inf);
    while(true) {
        vector<array<int,3>>query;
        for(int i = 0; i < Q; i++) {
            if(l[i]+1 < r[i]) {
                int mid = (l[i]+r[i])/2;
                query.push_back({mid,1,i});
            }
        }
        if(query.empty()) break;
        for(int i = 0; i < N; i++) {
            query.push_back({A[i],0,i});
        }
        sort(query.begin(),query.end());
        SegmentTree Seg(N);
        for(int i = 0; i < query.size(); i++) {
            if(query[i][1] == 0) {
                Seg.update(query[i][2]);
            }
            else {
                int id = query[i][2];
                array<int,4> now = Seg.query(L[id],R[id]+1);
                if(query[i][0] == 7) {
                    cout << now[0] << " " << now[1] << " " << now[2] << " " << now[3] << endl;
                }
                if(-now[2]+max(0,now[3]-1) >= 1) {
                    r[id] = query[i][0];
                }
                else {
                    l[id] = query[i][0];
                }
            }
        }
    }
    for(int i = 0; i < Q; i++) {
        cout << r[i] << "\n";
    }
}