#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vi vector<int>
#define vl vector<ll>
#define ov3(a, b, c, name, ...) name
#define rep0(n) for(ll aaaaa = 0; aaaaa < n; ++aaaaa)
#define rep1(i, n) for(ll i = 0; i < (n); i++)
#define rep2(i, a, b) for(ll i = (a); i < (b); i++)
#define rep(...) ov3(__VA_ARGS__, rep2, rep1, rep0)(__VA_ARGS__)
#define per(i, a, b) for(ll i = (a) - 1; i >= b; i--)
#define fore(e, v) for(auto &&e : v)
#define all(a) begin(a), end(a)
#define si(a) (int)(size(a))
bool chmin(auto &a, auto b) { return a > b ? a = b, 1 : 0; }
bool chmax(auto &a, auto b) { return a < b ? a = b, 1 : 0; }

#define pb push_back
#define eb emplace_back
#define i128 __int128_t

const ll inf = LLONG_MAX / 3;

template <typename S, S (*op)(S, S), S (*e)()> struct segtree {
    segtree(int n) : segtree(vector<S>(n, e())) {}
    segtree(const vector<S> &v) : n(si(v)) {
        s = bit_ceil(unsigned(n));
        log = countr_zero(unsigned(s));
        d = vector<S>(2 * s, e());
        rep(i, n) d[s + i] = v[i];
        per(i, s, 1) update(i);
    }
    void set(int p, S x) {
        d[p += s] = x;
        rep(i, 1, log + 1) update(p >> i);
    }
    S prod(int l, int r) const {
        S sml = e(), smr = e();
        l += s, r += s;
        while(l < r) {
            if(l & 1) sml = op(sml, d[l++]);
            if(r & 1) smr = op(d[--r], smr);
            l >>= 1, r >>= 1;
        }
        return op(sml, smr);
    }
    S all_prod() const { return d[1]; }

  private:
    int n, s, log;
    vector<S> d;
    void update(int k) { d[k] = op(d[k * 2], d[k * 2 + 1]); }
};

ll f(ll x, ll y) { return max(x, y); }
ll e() { return -inf; }

struct backet{
    const ll B = 300;
    vl a;
    vl b;
    void init(ll n){
        a.resize(n);
        b.resize(n);
        rep(i,n){
            a[i] = -inf;
            b[i] = -inf;
        }
    }
    void set(ll i,ll x){
        //chmax
        if(a[i] >= x)return;
        a[i] = x;
        chmax(b[i / B],x);
    }
    ll prod(ll r){
        r--;
        ll j = r / B;
        ll res = -inf;
        rep(i,j)chmax(res,b[i]);
        for(ll i = j * B;i <= r;i++){
            chmax(res,a[i]);
        }
        return res;
    }
};

#include <bits/extc++.h>
struct chash {
    const uint64_t C = (ll)(4e18 * acos(0)) | 71;
    ll operator()(ll x) const { return __builtin_bswap64(x * C); }
};
using namespace __gnu_pbds;
template <class T, class S> using hash_map = gp_hash_table<T, S, chash>;

int main() {
    cin.tie(0)->sync_with_stdio(0);
    ll n, q;
    cin >> n >> q;
    const ll m = 1e6 + 1;
    vl a(n);
    vector<vl> divs(n);
    rep(i, n) {
        cin >> a[i];
        for(ll x = 1; x * x <= a[i]; x++)
            if(a[i] % x == 0) {
                ll y = a[i] / x;
                divs[i].pb(x);
                if(x != y) divs[i].pb(y);
            }
    }
    vector<hash_map<ll, ll>> js(n);
    {
        vector<vl> is(m);
        rep(j, n) {
            fore(g, divs[j]) {
                while(si(is[g])) {
                    ll i = is[g].back();
                    is[g].pop_back();
                    js[i][g] = j;
                    // cout<<"i,j,g = "<<i<<" "<<j<<" "<<g<<endl;
                }
            }
            fore(g, divs[j]) { is[g].pb(j); }
        }
    }
    vector<hash_map<ll, ll>> ks(n);
    {
        vector<vl> is(m);
        vector<vector<pll>> qs(n);
        rep(i, n) {
            fore(g, divs[i]) {
                if(js[i].find(g) == js[i].end()) continue;
                ll j = js[i][g];
                // cout<<"i,j,g = "<<i<<" "<<j<<" "<<g<<endl;
                if(2 * j - i < n) { qs[2 * j - i].eb(i, g); }
            }
        }
        rep(k, n) {
            for(auto &&[i, g] : qs[k]) { is[g].pb(i); }
            fore(g, divs[k]) {
                while(si(is[g])) {
                    ll i = is[g].back();
                    is[g].pop_back();
                    ks[i][g] = k;
                }
            }
        }
    }

    vl l(q), r(q);
    rep(i, q) {
        cin >> l[i] >> r[i];
        l[i]--;
    }
    vector<vl> qs(n);
    rep(i, q) { qs[l[i]].pb(i); }
    // segtree<ll, f, e> seg(n);
    backet bc;
    bc.init(n);
    vl ans(q);
    for(ll i = n - 1; i >= 0; i--) {
        for(auto &&[g, k] : ks[i]) {
            bc.set(k,g);
        }
        fore(j, qs[i]) { ans[j] = bc.prod(r[j]); }
    }
    rep(i, q) { cout << ans[i] << "\n"; }
    // rep(i,n){
    //     for(auto &&[g,k] : ks[i]){
    //         ll j = js[i][g];
    //         cout<<i<<" "<<j<<" "<<k<<" "<<g<<endl;
    //     }
    // }
}