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.

import java.io.*;
import java.util.*;
import java.math.*;
public class Main{
    static StreamTokenizer in=new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    static Scanner sc=new Scanner(System.in);
    static int inf=1<<29;
    static int n,m,q;
    static int a[],b[],num[];
    static boolean used[];
    static int temp[],len;
    static int ans[];
    static ArrayList<Integer> map[];
    public static void  main(String args[])throws Exception{
        n=getInt();
        m=getInt();
        q=getInt();
        init();
        for(int i=1;i<=n;i++){
            int aa=getInt();
            a[aa]=i;
        }
        for(int i=0;i<m;i++){
            b[i]=a[getInt()];
        }
        for(int i=m-1;i>=0;i--){
            //System.out.println(num[b[i]%n+1]+" "+i);
            if(num[b[i]%n+1]!=-1)
                map[num[b[i]%n+1]].add(i);
            num[b[i]]=i;
        }
        for(int i=m-1;i>=0;i--){
            if(!used[i]){
                dfs(i);
            }
        }
        /*for(int i=0;i<m;i++){
            System.out.println(ans[i]);
        }*/
        for(int i=m-2;i>=0;i--){
            ans[i]=Math.min(ans[i],ans[i+1]);
        }
        while(q--!=0){
            int l=getInt()-1;
            int r=getInt()-1;
            if(ans[l]<=r){
                out.write("1");
            }else{
                out.write("0");
            }
        }
        out.flush();
        out.close();
    }
    public static void dfs(int i){
        //System.out.println(i);
        used[i]=true;
        temp[len++]=i;
        if(len>=n){
            ans[i]=temp[len-n];
            //System.out.println(i+" "+temp[len-n]);
        }
        for(int j=0;j<map[i].size();j++){
            dfs(map[i].get(j));
        }
        len--;
    }
    public  static void init(){
        a=new int[n+1];
        b=new int[m];
        num=new int[n+1];
        used=new boolean[m+1];
        ans=new int[m];
        map=new ArrayList[m];
        temp=new int[m+10];
        for(int i=0;i<m;i++){
            map[i]=new ArrayList<Integer>();
            ans[i]=inf;
        }
        for(int i=0;i<=n;i++){
            num[i]=-1;
        }
    }
    public static int getInt()throws Exception{
        in.nextToken();
        return (int)in.nval;
    }
}