#include <bits/stdc++.h>
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"
#define NDEBUG
#define SHOW(...) static_cast<void>(0)
//!===========================================================!//
//!  dP     dP                          dP                    !//
//!  88     88                          88                    !//
//!  88aaaaa88a .d8888b. .d8888b. .d888b88 .d8888b. 88d888b.  !//
//!  88     88  88ooood8 88'  '88 88'  '88 88ooood8 88'  '88  !//
//!  88     88  88.  ... 88.  .88 88.  .88 88.  ... 88        !//
//!  dP     dP  '88888P' '88888P8 '88888P8 '88888P' dP        !//
//!===========================================================!//
template <typename T>
T read()
{
    T v;
    return std::cin >> v, v;
}
template <typename T>
std::vector<T> readVec(const std::size_t l)
{
    std::vector<T> v(l);
    for (auto& e : v) { std::cin >> e; }
    return v;
}
using ld = long double;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr unsigned int MOD = 1000000007;
template <typename T>
constexpr T INF = std::numeric_limits<T>::max() / 4;
template <typename F>
constexpr F PI = static_cast<F>(3.1415926535897932385);
std::mt19937 mt{std::random_device{}()};
template <typename T>
bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }
template <typename T>
bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }
template <typename T>
std::vector<T> Vec(const std::size_t n, T v) { return std::vector<T>(n, v); }
template <class... Args>
auto Vec(const std::size_t n, Args... args) { return std::vector<decltype(Vec(args...))>(n, Vec(args...)); }
template <typename T>
constexpr T popCount(const T u)
{
#ifdef __has_builtin
    return u == 0 ? T(0) : (T)__builtin_popcountll(u);
#else
    unsigned long long v = static_cast<unsigned long long>(u);
    return v = (v & 0x5555555555555555ULL) + (v >> 1 & 0x5555555555555555ULL), v = (v & 0x3333333333333333ULL) + (v >> 2 & 0x3333333333333333ULL), v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL, static_cast<T>(v * 0x0101010101010101ULL >> 56 & 0x7f);
#endif
}
template <typename T>
constexpr T log2p1(const T u)
{
#ifdef __has_builtin
    return u == 0 ? T(0) : T(64 - __builtin_clzll(u));
#else
    unsigned long long v = static_cast<unsigned long long>(u);
    return v = static_cast<unsigned long long>(v), v |= (v >> 1), v |= (v >> 2), v |= (v >> 4), v |= (v >> 8), v |= (v >> 16), v |= (v >> 32), popCount(v);
#endif
}
template <typename T>
constexpr T clog(const T v) { return v == 0 ? T(0) : log2p1(v - 1); }
template <typename T>
constexpr T msbp1(const T v) { return log2p1(v); }
template <typename T>
constexpr T lsbp1(const T v)
{
#ifdef __has_builtin
    return __builtin_ffsll(v);
#else
    return v == 0 ? T(0) : popCount((v & (-v)) - T(1)) + T(1);
#endif
}
template <typename T>
constexpr bool ispow2(const T v) { return popCount(v) == 1; }
template <typename T>
constexpr T ceil2(const T v) { return v == 0 ? T(1) : T(1) << log2p1(v - 1); }
template <typename T>
constexpr T floor2(const T v) { return v == 0 ? T(0) : T(1) << (log2p1(v) - 1); }
//!===============================================================!//
//!   88888888b            dP       .88888.   a88888b. 888888ba   !//
//!   88                   88      d8'   '88 d8'   '88 88    '8b  !//
//!  a88aaaa    dP.  .dP d8888P    88        88        88     88  !//
//!   88         '8bd8'    88      88   YP88 88        88     88  !//
//!   88         .d88b.    88      Y8.   .88 Y8.   .88 88    .8P  !//
//!   88888888P dP'  'dP   dP       '88888'   Y88888P' 8888888P   !//
//!===============================================================!//
template <typename T>
constexpr std::pair<T, T> extgcd(const T a, const T b)
{
    if (b == 0) { return std::pair<T, T>{1, 0}; }
    const auto p = extgcd(b, a % b);
    return {p.second, p.first - p.second * (a / b)};
}
template <typename T>
constexpr T inverse(const T a, const T mod) { return (mod + extgcd((mod + a % mod) % mod, mod).first % mod) % mod; }
//!========================================================!//
//!  8888ba.88ba                 dP    dP            dP    !//
//!  88  '8b  '8b                88    88            88    !//
//!  88   88   88 .d8888b. .d888b88    88 88d888b. d8888P  !//
//!  88   88   88 88'  '88 88'  '88    88 88'  '88   88    !//
//!  88   88   88 88.  .88 88.  .88    88 88    88   88    !//
//!  dP   dP   dP '88888P' '88888P8    dP dP    dP   dP    !//
//!========================================================!//
template <uint mod>
class ModInt
{
private:
    uint v;
    static uint norm(const uint& x) { return x < mod ? x : x - mod; }
    static ModInt make(const uint& x)
    {
        ModInt m;
        return m.v = x, m;
    }
    static ModInt power(ModInt x, ll n)
    {
        ModInt ans = 1;
        for (; n; n >>= 1, x *= x) {
            if (n & 1) { ans *= x; }
        }
        return ans;
    }
    static ModInt inv(const ModInt& x) { return ModInt{inverse((ll)x.v, (ll)mod)}; }

public:
    ModInt() : v{0} {}
    ModInt(const ll val) : v{norm(uint(val % (ll)mod + (ll)mod))} {}
    ModInt(const ModInt<mod>& n) : v{n()} {}
    explicit operator bool() const { return v != 0; }
    ModInt<mod>& operator=(const ModInt<mod>& n) { return v = n(), (*this); }
    ModInt<mod>& operator=(const ll val) { return v = norm(uint(val % (ll)mod + (ll)mod)), (*this); }
    ModInt<mod> operator+() const { return *this; }
    ModInt<mod> operator-() const { return make(norm(mod - v)); }
    ModInt<mod> operator+(const ModInt<mod>& val) const { return make(norm(v + val())); }
    ModInt<mod> operator-(const ModInt<mod>& val) const { return make(norm(v + mod - val())); }
    ModInt<mod> operator*(const ModInt<mod>& val) const { return make((uint)((ll)v * val() % (ll)mod)); }
    ModInt<mod> operator/(const ModInt<mod>& val) const { return *this * inv(val()); }
    ModInt<mod>& operator+=(const ModInt<mod>& val) { return *this = *this + val; }
    ModInt<mod>& operator-=(const ModInt<mod>& val) { return *this = *this - val; }
    ModInt<mod>& operator*=(const ModInt<mod>& val) { return *this = *this * val; }
    ModInt<mod>& operator/=(const ModInt<mod>& val) { return *this = *this / val; }
    ModInt<mod> operator+(const ll val) const { return ModInt{v + val}; }
    ModInt<mod> operator-(const ll val) const { return ModInt{v - val}; }
    ModInt<mod> operator*(const ll val) const { return ModInt{(ll)v * (val % mod)}; }
    ModInt<mod> operator/(const ll val) const { return ModInt{(ll)v * inv(val)}; }
    template <typename I>
    ModInt<mod> operator^(const I n) const { return power(v, n); }
    ModInt<mod>& operator+=(const ll val) { return *this = *this + val; }
    ModInt<mod>& operator-=(const ll val) { return *this = *this - val; }
    ModInt<mod>& operator*=(const ll val) { return *this = *this * val; }
    ModInt<mod>& operator/=(const ll val) { return *this = *this / val; }
    template <typename I>
    ModInt<mod>& operator^=(const I n) { return (*this) = ((*this) ^ n); }
    bool operator==(const ModInt<mod>& val) const { return v == val.v; }
    bool operator!=(const ModInt<mod>& val) const { return not(*this == val); }
    bool operator==(const ll val) const { return v == norm(uint((ll)mod + val % (ll)mod)); }
    bool operator!=(const ll val) const { return not(*this == val); }
    uint operator()() const { return v; }
};
template <uint mod>
inline ModInt<mod> operator+(const ll val, const ModInt<mod>& n) { return n + val; }
template <uint mod>
inline ModInt<mod> operator-(const ll val, const ModInt<mod>& n) { return ModInt<mod>{val - (ll)n()}; }
template <uint mod>
inline ModInt<mod> operator*(const ll val, const ModInt<mod>& n) { return n * val; }
template <uint mod>
inline ModInt<mod> operator/(const ll val, const ModInt<mod>& n) { return ModInt<mod>(val) / n; }
template <uint mod>
inline bool operator==(const ll val, const ModInt<mod>& n) { return n == val; }
template <uint mod>
inline bool operator!=(const ll val, const ModInt<mod>& n) { return not(val == n); }
template <uint mod>
inline std::istream& operator>>(std::istream& is, ModInt<mod>& n)
{
    uint v;
    return is >> v, n = v, is;
}
template <uint mod>
std::ostream& operator<<(std::ostream& os, const ModInt<mod>& n) { return (os << n()); }
//!====================================================================================================!//
//!  .d88888b                                                  d888888P          dP       dP           !//
//!  88.    "'                                                    88             88       88           !//
//!  'Y88888b. 88d888b. .d8888b. 88d888b. .d8888b. .d8888b.       88    .d8888b. 88d888b. 88 .d8888b.  !//
//!        '8b 88'  '88 88'  '88 88'  '88 Y8ooooo. 88ooood8       88    88'  '88 88'  '88 88 88ooood8  !//
//!  d8'   .8P 88.  .88 88.  .88 88             88 88.  ...       88    88.  .88 88.  .88 88 88.  ...  !//
//!   Y88888P  88Y888P' '88888P8 dP       '88888P' '88888P'       dP    '88888P8 88Y8888' dP '88888P'  !//
//!            88                                                                                      !//
//!            dP                                                                                      !//
//!====================================================================================================!//
template <typename SemiGroup>
class SparseTable
{
public:
    using ValType = typename SemiGroup::ValType;
    template <typename InIt>
    SparseTable(const InIt first, const InIt last) : D(clog(std::size_t(std::distance(first, last)) + 1)), table(D, std::vector<ValType>(1 << D))
    {
        const std::size_t N = 1 << D;
        for (std::size_t d = 0, B = 1; d < D; d++, B <<= 1) {
            std::copy(first, last, table[d].begin());
            for (std::size_t b = 0; b < N / B; b++) {
                if (b % 2 == 1) {
                    for (std::size_t i = 1; i < B; i++) { table[d][b * B + i] = op(table[d][b * B + i - 1], table[d][b * B + i]); }
                } else {
                    for (std::size_t i = 1; i < B; i++) { table[d][(b + 1) * B - i - 1] = op(table[d][(b + 1) * B - i - 1], table[d][(b + 1) * B - i]); }
                }
            }
        }
    }
    ValType fold(const std::size_t l, const std::size_t r) const
    {
        assert(l < r);
        if (r - l == 1) { return table[0][l]; }
        const std::size_t d = msbp1(r ^ l) - 1;
        return op(table[d][l], table[d][r - 1]);
    }

private:
    const std::size_t D;
    std::vector<std::vector<ValType>> table;
    const SemiGroup op{};
};
//!=====================================!//
//!  8888ba.88ba           oo           !//
//!  88  '8b  '8b                       !//
//!  88   88   88 .d8888b. dP 88d888b.  !//
//!  88   88   88 88'  '88 88 88'  '88  !//
//!  88   88   88 88.  .88 88 88    88  !//
//!  dP   dP   dP '88888P8 dP dP    dP  !//
//!=====================================!//
constexpr ll gcd(const ll a, const ll b) { return (b != 0) ? gcd(b, a % b) : a; }
constexpr ll lcm(const ll a, const ll b) { return (a == 0 and b == 0) ? 0 : (a / gcd(a, b)) * b; }
int main()
{
    using mint = ModInt<MOD>;
    const int N = read<int>(), Q = read<int>();
    std::vector<int> P(N + 1, 0);
    for (int i = 1; i <= N; i++) { std::cin >> P[i]; }
    std::vector<int> sz(N + 1, 0);
    auto imos = Vec(41, N + 1, 0);
    std::vector<mint> sum(N + 1, 0);
    for (int i = 1; i <= N; i++) {
        sz[i] = 1, sum[i] = i;
        for (int p = P[i]; p != i; p = P[p]) { sz[i]++, sum[i] += p; };
        sum[i] /= sz[i], imos[sz[i]][i] = 1;
    }
    for (int i = 0; i <= 40; i++) {
        for (int j = 1; j <= N; j++) { imos[i][j] += imos[i][j - 1]; }
    }
    for (int i = 1; i <= N; i++) { sum[i] += sum[i - 1]; }
    auto exist = [&](const int sz, const int l, const int r) { return imos[sz][r] - imos[sz][l - 1]; };
    auto fold = [&](const int l, const int r) { return sum[r] - sum[l - 1]; };
    struct GCD
    {
        using ValType = ll;
        ValType operator()(const ValType& a, const ValType& b) const { return lcm(a, b); }
    };
    SparseTable<GCD> stable(sz.begin(), sz.end());
    auto lcm = [&](const int l, const int r) -> mint { return mint(stable.fold(l, r + 1)); };
    auto query = [&](const int l, const int r) -> mint { return fold(l, r) * lcm(l, r); };
    for (int q = 0, l, r; q < Q; q++) { std::cin >> l >> r, std::cout << query(l, r) << std::endl; }
    return 0;
}



Measured memory_bytes: 38672