Recently Lynyrd and Skynyrd went to a shop where Lynyrd bought a permutation p of length n, and Skynyrd bought an array a of length m, consisting of integers from 1 to n. 

Lynyrd and Skynyrd became bored, so they asked you q queries, each of which has the following form: "does the subsegment of a from the l-th to the r-th positions, inclusive, have a subsequence that is a cyclic shift of p?" Please answer the queries.

A permutation of length n is a sequence of n integers such that each integer from 1 to n appears exactly once in it.

A cyclic shift of a permutation (p_1, p_2, …, p_n) is a permutation (p_i, p_{i + 1}, …, p_{n}, p_1, p_2, …, p_{i - 1}) for some i from 1 to n. For example, a permutation (2, 1, 3) has three distinct cyclic shifts: (2, 1, 3), (1, 3, 2), (3, 2, 1).

A subsequence of a subsegment of array a from the l-th to the r-th positions, inclusive, is a sequence a_{i_1}, a_{i_2}, …, a_{i_k} for some i_1, i_2, …, i_k such that l ≤ i_1 < i_2 < … < i_k ≤ r.

Input

The first line contains three integers n, m, q (1 ≤ n, m, q ≤ 2 ⋅ 10^5) — the length of the permutation p, the length of the array a and the number of queries.

The next line contains n integers from 1 to n, where the i-th of them is the i-th element of the permutation. Each integer from 1 to n appears exactly once.

The next line contains m integers from 1 to n, the i-th of them is the i-th element of the array a.

The next q lines describe queries. The i-th of these lines contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m), meaning that the i-th query is about the subsegment of the array from the l_i-th to the r_i-th positions, inclusive.

Output

Print a single string of length q, consisting of 0 and 1, the digit on the i-th positions should be 1, if the subsegment of array a from the l_i-th to the r_i-th positions, inclusive, contains a subsequence that is a cyclic shift of p, and 0 otherwise.

Examples

Input

3 6 3
2 1 3
1 2 3 1 2 3
1 5
2 6
3 5


Output

110


Input

2 4 3
2 1
1 1 2 2
1 2
2 3
3 4


Output

010

Note

In the first example the segment from the 1-st to the 5-th positions is 1, 2, 3, 1, 2. There is a subsequence 1, 3, 2 that is a cyclic shift of the permutation. The subsegment from the 2-nd to the 6-th positions also contains a subsequence 2, 1, 3 that is equal to the permutation. The subsegment from the 3-rd to the 5-th positions is 3, 1, 2, there is only one subsequence of length 3 (3, 1, 2), but it is not a cyclic shift of the permutation.

In the second example the possible cyclic shifts are 1, 2 and 2, 1. The subsegment from the 1-st to the 2-nd positions is 1, 1, its subsequences are not cyclic shifts of the permutation. The subsegment from the 2-nd to the 3-rd positions is 1, 2, it coincides with the permutation. The subsegment from the 3 to the 4 positions is 2, 2, its subsequences are not cyclic shifts of the permutation.
#include <bits/stdc++.h>
using namespace std;
const int MaxN = 200100;
const int LOG = 20;
const int Mod = 1e9 + 7;
const int INF = 1e9;
int najveca_pot[MaxN];
int maxs[LOG][MaxN];
int anc[MaxN][LOG];
int p[MaxN];
int nextt[MaxN], prevv[MaxN];
int z[MaxN];
int lastTime[MaxN];
int N, M, Q;
int query(int a, int b) {
  int ret = -1;
  for (int k = (a); k < (b); k++) {
    ret = max(maxs[0][k], ret);
  }
  return ret;
}
int queryKonst(int a, int b) {
  int naj_pot = najveca_pot[b - a];
  return max(maxs[naj_pot][a], maxs[naj_pot][b - (1 << naj_pot)]);
}
void init2() {
  najveca_pot[1] = 0;
  for (int i = 2; i < MaxN; ++i) najveca_pot[i] = najveca_pot[i / 2] + 1;
}
void init() {
  for (int pot = 0; (1 << pot) <= M; ++pot) {
    for (int i = 0; i < M; ++i) {
      maxs[pot + 1][i] =
          max(maxs[pot][i],
              (i + (1 << pot)) < M ? maxs[pot][i + (1 << pot)] : -INF);
    }
  }
}
void solve() {
  init();
  init2();
  for (int i = (0); i < (Q); i++) {
    int l, r;
    cin >> l >> r;
    l--;
    r--;
    if (N == 1) {
      cout << 1;
      continue;
    }
    cout << ((queryKonst(l, r + 1) >= l) ? 1 : 0);
  }
  cout << endl;
}
void prec() {
  for (int k = (0); k < (M); k++)
    for (int w = (0); w < (LOG); w++) anc[k][w] = -1;
  for (int i = (1); i < (N + 1); i++) lastTime[i] = -1;
  for (int k = (0); k < (M); k++) {
    lastTime[z[k]] = k;
    int lastPrev = lastTime[prevv[z[k]]];
    anc[k][0] = lastPrev;
  }
  for (int w = (1); w < (LOG); w++) {
    for (int k = (0); k < (M); k++) {
      int lastAnc = anc[k][w - 1];
      if (lastAnc != -1) {
        anc[k][w] = anc[lastAnc][w - 1];
      }
    }
  }
  for (int k = (0); k < (M); k++) {
    int cur = k;
    int len = N - 1;
    for (int w = LOG - 1; w >= 0; w--) {
      if (len < (1 << w)) continue;
      len -= (1 << w);
      cur = anc[cur][w];
      if (cur == -1) break;
    }
    if (len == 0) {
      maxs[0][k] = cur;
    } else {
      assert(cur == -1);
      maxs[0][k] = -1;
    }
  }
}
void load() {
  cin >> N >> M >> Q;
  for (int i = (0); i < (N); i++) {
    cin >> p[i + 1];
  }
  for (int k = (0); k < (M); k++) cin >> z[k];
  for (int i = (1); i < (N); i++) {
    nextt[p[i]] = p[i + 1];
    prevv[p[i + 1]] = p[i];
  }
  nextt[p[N]] = p[1];
  prevv[p[1]] = p[N];
}
int main() {
  ios_base::sync_with_stdio(false);
  load();
  prec();
  solve();
  return 0;
}
