#include <bits/stdc++.h>

using namespace std;

#define REP(i, n) for (int i=0; i<(n); ++i)
#define RREP(i, n) for (int i=(int)(n)-1; i>=0; --i)
#define FOR(i, a, n) for (int i=(a); i<(n); ++i)
#define RFOR(i, a, n) for (int i=(int)(n)-1; i>=(a); --i)

#define SZ(x) ((int)(x).size())
#define all(x) begin(x),end(x)

#define dump(x) cerr<<#x<<" = "<<(x)<<endl
#define debug(x) cerr<<#x<<" = "<<(x)<<" (L"<<__LINE__<<")"<<endl;

template<class T>
ostream &operator<<(ostream &os, const vector <T> &v) {
    os << "[";
    REP(i, SZ(v)) {
        if (i) os << ", ";
        os << v[i];
    }
    return os << "]";
}

template<class T, class U>
ostream &operator<<(ostream &os, const pair <T, U> &p) {
    return os << "(" << p.first << " " << p.second << ")";
}

template<class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
bool chmin(T &a, const T &b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using P = pair<int, int>;
using vi = vector<int>;
using vll = vector<ll>;
using vvi = vector<vi>;
using vvll = vector<vll>;

const ll MOD = 1e9 + 7;
const int INF = INT_MAX / 2;
const ll LINF = LLONG_MAX / 2;
const ld eps = 1e-9;


template<int64_t mod>
struct modint {
    using LL = int64_t;
    LL val;
    modint(LL val=0) : val(((val % mod) + mod) % mod) {}

    const modint operator+() const { return *this; }
    const modint operator-() const { return (-val + mod) % mod; }
    const modint inv() const { return pow(mod-2); }

    modint& operator+=(const modint& rhs) {
        (val += rhs.val) %= mod;
        return *this;
    }
    modint& operator-=(const modint& rhs) {
        return *this += -rhs;
    }
    modint& operator*=(const modint& rhs) {
        (val *= rhs.val) %= mod;
        return *this;
    }
    modint& operator/=(const modint& rhs) {
        return *this *= rhs.inv();
    }

    const modint operator+(const modint& rhs) const {
        return modint(*this) += rhs;
    }
    const modint operator-(const modint& rhs) const {
        return modint(*this) -= rhs;
    }
    const modint operator*(const modint& rhs) const {
        return modint(*this) *= rhs;
    }
    const modint operator/(const modint& rhs) const {
        return modint(*this) /= rhs;
    }

    const modint pow(LL n) const {
        modint ret = 1, tmp = val;
        while (n) {
            if (n & 1) ret *= tmp;
            tmp *= tmp; n >>= 1;
        }
        return ret;
    }

    bool operator==(const modint& rhs) const { return val == rhs.val; }
    bool operator!=(const modint& rhs) const { return !(*this == rhs); }

    friend const modint operator+(const LL& lhs, const modint& rhs) {
        return modint(lhs) + rhs;
    }
    friend const modint operator-(const LL& lhs, const modint& rhs) {
        return modint(lhs) - rhs;
    }
    friend const modint operator*(const LL& lhs, const modint& rhs) {
        return modint(lhs) * rhs;
    }
    friend const modint operator/(const LL& lhs, const modint& rhs) {
        return modint(lhs) / rhs;
    }

    friend bool operator==(const LL& lhs, const modint& rhs) {
        return modint(lhs) == rhs;
    }
    friend bool operator!=(const LL& lhs, const modint& rhs) {
        return modint(lhs) != rhs;
    }

    friend ostream& operator<<(ostream& os, const modint& a) {
        return os << a.val;
    }
    friend istream& operator>>(istream& is, modint& a) {
        LL tmp; is >> tmp;
        a = tmp;
        return is;
    }
};



template<typename M>
struct SegmentTree {
    int n, sz;
    vector<M> data;
    const function<M(M,M)> f;
    const M e;

    SegmentTree(
            int n,
            const function<M(M,M)>& f,
            const M& e
    ) : n(n), f(f), e(e) {
        sz = 1;
        while (sz < n) sz <<= 1;
        data.assign(2*sz, e);
    }

    void build(const vector<M>& v) {
        assert(v.size() <= n);
        for (int i = 0; i < v.size(); ++i) {
            data[i + sz] = v[i];
        }
        for (int i = sz-1; i > 0; --i) {
            data[i] = f(data[2*i], data[2*i+1]);
        }
    }

    template<typename UpdateQuery>
    void update(int k, const UpdateQuery& q) {
        k += sz;
        data[k] = q(data[k]);
        while (k >>= 1) {
            data[k] = f(data[2*k], data[2*k+1]);
        }
    }

    M _query(int a, int b, int k, int l, int r) const {
        if (r <= a or b <= l) return e;
        if (a <= l and r <= b) return data[k];
        return f(_query(a,b,2*k,  l,(l+r)/2),
                 _query(a,b,2*k+1,(l+r)/2,r));
    }

    M query(int a, int b) const {
        // return f[a,b)
        return _query(a, b, 1, 0, sz);
    }

    M operator[](int i) const {
        return data.at(i + sz);
    }

    friend ostream& operator<<(ostream& os, const SegmentTree& s) {
        os << "[";
        for (int i = 0; i < s.n; ++i) {
            if (i) os << " ";
            os << s[i];
        }
        return os << "]";
    }
};



int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);

    using Int = modint<MOD>;

    int N, Q; cin >> N >> Q;
    vi p(N);
    REP(i, N) {
        cin >> p[i]; --p[i];
    }

    int cnt = 0;
    vi used(N, -1);
    map<int,int> T, S;
    REP(i, N) {
        if (used[i] != -1) continue;
        int now = i;
        while (used[now] == -1) {
            ++T[cnt];
            S[cnt] += now + 1;
            used[now] = cnt;
            now = p[now];
        }
        ++cnt;
    }
    // for (auto& tp : T) debug(tp);
    // cerr << endl;
    // for (auto& tp : S) debug(tp);
    // debug(used);

    SegmentTree<Int> sum(N, [](Int a, Int b){ return a+b; }, 0);
    vector<Int> datasum(N);
    REP(i, N) {
        datasum[i] = Int(S[used[i]]) / T[used[i]];
    }
    // debug(datasum);
    sum.build(datasum);

    SegmentTree<map<int,int>> lcm(N, [](map<int,int> a, map<int,int> b){
        if (a.size() < b.size()) swap(a, b);
        for (auto &tp : b) {
            chmax(a[tp.first], tp.second);
        }
        return a;
    }, map<int,int>());

    map<int,map<int,int>> factorize;
    for (auto tp : T) {
        for (int i = 2; i * i <= tp.second; ++i) {
            while (tp.second % i == 0) {
                tp.second /= i;
                ++factorize[tp.first][i];
            }
        }
        if (tp.second > 1) {
            ++factorize[tp.first][tp.second];
        }
    }
    // for (auto &tp : factorize) {
    //     debug(tp.first);
    //     for (auto &ttp : tp.second) {
    //         debug(ttp);
    //     }
    //     cerr << endl;
    // }
    vector<map<int,int>> datalcm(N);
    REP(i, N) {
        datalcm[i] = factorize[used[i]];
    }
    lcm.build(datalcm);

    while (Q--) {
        int l, r; cin >> l >> r;
        Int s = sum.query(l-1, r);
        auto mp = lcm.query(l-1, r);
        Int LCM = 1;
        for (auto &tp : mp) {
            LCM *= Int(tp.first).pow(tp.second);
        }
        cout << s * LCM << endl;
        // debug(s);
        // debug(LCM);
        // debug(s * LCM);
    }

    return 0;
}



Measured memory_bytes: 61636