#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; }

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<unordered_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<unordered_map<ll,ll> > ks(n);
    {
        vector<vl> is(m);
        vector<vector<pll> > qs(n);
        rep(i,n){
            fore(g,divs[i]){
                if(!js[i].count(g))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);
    vl ans(q);
    for(ll i = n - 1;i >= 0;i--){
        for(auto &&[g,k] : ks[i]){
            ll cur = seg.prod(k, k + 1);
            if(cur < g){
                seg.set(k,g);
            }
        }
        fore(j,qs[i]){
            ans[j] = seg.prod(l[j], 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;
    //     }
    // }
}