Problem: Priests of the Quetzalcoatl cult want to build a tower to represent a power of their god. Tower is usually made of power-charged rocks. It is built with the help of rare magic by levitating the current top of tower and adding rocks at its bottom. If top, which is built from k - 1 rocks, possesses power p and we want to add the rock charged with power wk then value of power of a new tower will be {wk}p. 

Rocks are added from the last to the first. That is for sequence w1, ..., wm value of power will be

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After tower is built, its power may be extremely large. But still priests want to get some information about it, namely they want to know a number called cumulative power which is the true value of power taken modulo m. Priests have n rocks numbered from 1 to n. They ask you to calculate which value of cumulative power will the tower possess if they will build it from rocks numbered l, l + 1, ..., r. 

Input

First line of input contains two integers n (1 ≤ n ≤ 105) and m (1 ≤ m ≤ 109).

Second line of input contains n integers wk (1 ≤ wk ≤ 109) which is the power of rocks that priests have.

Third line of input contains single integer q (1 ≤ q ≤ 105) which is amount of queries from priests to you.

kth of next q lines contains two integers lk and rk (1 ≤ lk ≤ rk ≤ n). 

Output

Output q integers. k-th of them must be the amount of cumulative power the tower will have if is built from rocks lk, lk + 1, ..., rk.

Example

Input

6 1000000000
1 2 2 3 3 3
8
1 1
1 6
2 2
2 3
2 4
4 4
4 5
4 6


Output

1
1
2
4
256
3
27
597484987

Note

327 = 7625597484987

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using namespace rel_ops;
using ll = int64_t;
using Vi = vector<int>;
using Pii = pair<int, int>;
void dbgx(...) {}
template <class T, class U = int, class... V>
void dbgx(T s, U a, V... b) {
  while (*s && *s != ',') cerr << *s++;
  cerr << ": " << a << *s++;
  dbgx(s, b...);
}
template <class T, class U = int, class... V>
auto operator<<(ostream& o, T x) -> decltype(&T::print, cout) {
  x.print();
  return o;
}
template <class T, class U = int, class... V>
auto operator<<(ostream& o, pair<T, U> x) -> decltype(0, cout) {
  return o << "(" << x.first << ", " << x.second << ")";
}
template <class T, class U = int, class... V>
auto operator<<(ostream& o, T x) -> decltype(T().begin(), cout) {
  o << "[";
  for (auto& e : (x)) o << e << ", ";
  return o << "]";
}
ll nElems, mod;
vector<ll> elems, mods;
ll phi(ll n) {
  ll ret = n;
  for (ll p = 2; p * p <= n; p++) {
    if ((n % p) == 0) {
      while ((n % p) == 0) n /= p;
      ret -= ret / p;
    }
  }
  return (n > 1 ? ret - ret / n : ret);
}
ll modPow(ll base, ll exp, ll m) {
  ll ret = 1;
  base %= m;
  while (exp > 0) {
    if (exp & 1) ret = (ret * base) % m;
    base = (base * base) % m;
    exp >>= 1;
  }
  return ret % m;
}
ll tower(int begin, int end, int mi) {
  if (begin >= end || mi >= int((mods).size()) - 1) return 1;
  ll naive = 1;
  bool usePhi = false;
  int i = begin;
  while (i < end - 1 && i < begin + 5 && elems[i] != 1) i++;
  for (; i > begin; i--) {
    ll times = naive;
    naive = 1;
    if (elems[i] > 1) {
      for (int j = (0); j < (times); j++) {
        naive *= elems[i];
        if (naive >= 32) {
          usePhi = true;
          goto outLoop;
        }
      }
    }
  }
outLoop:;
  if (!usePhi) return modPow(elems[begin], naive, mods[mi]);
  ll p = tower(begin + 1, end, mi + 1);
  return modPow(elems[begin], mods[mi + 1] + (p % mods[mi + 1]), mods[mi]);
}
int main() {
  cin.sync_with_stdio(0);
  cin.tie(0);
  cout << fixed << setprecision(10);
  cin >> nElems >> mod;
  for (ll m = mod; m > 1; m = phi(m)) mods.push_back(m);
  mods.push_back(1);
  mods.push_back(1);
  elems.resize(nElems);
  for (auto& e : (elems)) cin >> e;
  int q;
  cin >> q;
  while (q--) {
    int begin, end;
    cin >> begin >> end;
    cout << tower(begin - 1, end, 0) << endl;
  }
  return 0;
}