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;
template <typename T>
void r1(T &x) {
  x = 0;
  char c(getchar());
  int f(1);
  for (; c < '0' || c > '9'; c = getchar())
    if (c == '-') f = -1;
  for (; '0' <= c && c <= '9'; c = getchar()) x = (x * 10) + (c ^ 48);
  x *= f;
}
const int maxn = 2e5 + 5;
const int maxm = maxn << 1;
const int mod = 1e9 + 7;
typedef int room[maxn];
template <int mod>
struct typemod {
  int z;
  typemod(int a = 0) : z(a) {}
  inline int inc(int a, int b) const {
    return a += b - mod, a + ((a >> 31) & mod);
  }
  inline int dec(int a, int b) const { return a -= b, a + ((a >> 31) & mod); }
  inline int mul(int a, int b) const { return 1ll * a * b % mod; }
  typemod<mod> operator+(const typemod<mod> &x) const {
    return typemod(inc(z, x.z));
  }
  typemod<mod> operator-(const typemod<mod> &x) const {
    return typemod(dec(z, x.z));
  }
  typemod<mod> operator*(const typemod<mod> &x) const {
    return typemod(mul(z, x.z));
  }
  typemod<mod> &operator+=(const typemod<mod> &x) {
    *this = *this + x;
    return *this;
  }
  typemod<mod> &operator-=(const typemod<mod> &x) {
    *this = *this - x;
    return *this;
  }
  typemod<mod> &operator*=(const typemod<mod> &x) {
    *this = *this * x;
    return *this;
  }
  int operator==(const typemod<mod> &x) const { return x.z == z; }
  int operator!=(const typemod<mod> &x) const { return x.z != z; }
};
int n, m, q, cnt;
room bef, p, a, near, pre, E, head;
struct Edge {
  int to, next;
} edg[maxn << 1];
void add(int u, int v) { edg[++cnt] = (Edge){v, head[u]}, head[u] = cnt; }
room dep, num, r;
void dfs(int p) {
  num[dep[p]] = p;
  if (dep[p] >= n)
    r[p] = num[dep[p] - (n - 1)];
  else
    r[p] = m + 1;
  for (int i = head[p]; i; i = edg[i].next) {
    int to = edg[i].to;
    dep[to] = dep[p] + 1;
    dfs(to);
  }
}
signed main() {
  int i, j;
  r1(n), r1(m), r1(q);
  for (i = 1; i <= n; ++i) {
    r1(p[i]), bef[p[i]] = p[i - 1];
  }
  bef[p[1]] = p[n];
  for (i = 1; i <= m; ++i) {
    r1(a[i]), pre[i] = near[a[i]], near[a[i]] = i;
    for (j = near[bef[a[i]]]; (j) && (E[j] == 0); j = pre[j]) E[j] = i;
  }
  for (i = 1; i <= m; ++i) add((E[i] == 0 ? m + 1 : E[i]), i);
  dfs(m + 1);
  for (i = m; i > 1; --i) r[i - 1] = min(r[i - 1], r[i]);
  while (q--) {
    int l, r;
    r1(l), r1(r);
    putchar('0' + (bool)(::r[l] <= r));
  }
  return 0;
}
