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.util.*;
import java.io.*;


public class answer{
    
    static class SparseTree{
        int n;
        int root;
        int[][] dp;
        int[] depth;
        SparseTree(int n,int m,LinkedList<Integer>[] al){
            this.n = n;
            root = m;
            dp = new int[20][n];
            depth = new int[n];
            for(int i=0;i<20;i++){
                Arrays.fill(dp[i],-1);
            }
            dfs(root,-1,al);
            depthDfs(root,-1,al);
        }
        void dfs(int m,int p,LinkedList<Integer>[] al){
            dp[0][m] = p;
            for(int i=1;i<20;i++){
                if(dp[i-1][m]!=-1)
                    dp[i][m] = dp[i-1][dp[i-1][m]];
            }
            for(int u:al[m])
                if(u!=p) dfs(u,m,al);
        }
        void depthDfs(int cur,int prev,LinkedList<Integer>[] al){
            if(prev==-1) depth[cur] = 0;
            else depth[cur] = depth[prev] + 1;
            for(int u:al[cur])
                if(u!=prev) depthDfs(u,cur,al);
        }
        int getDepth(int i){
            return depth[i];
        }
        
        int getParent(int node,int np){
            if(np==0) return node;
            if(np>depth[node]) return -1;
            for(int i=0;i<20;i++){
                if(((np>>i)&1)==1)
                    node = dp[i][node];
            }
            return node;
        }
        
    }
    
    
    static Node[] luckup;
    
    static class Node{
        int id;
        int next;
        LinkedList<Integer> children = new LinkedList<Integer>();
        Node(int id){
            this.id = id;
            next = 0;
        }
    }
    
    public static Node getNode(int id){
		return luckup[id];
	}
    
    static int[] next;
    static void build(int[] a,int m,int n){
        LinkedList<Integer>[] l = new LinkedList[n+1];
        for(int i=1;i<n+1;i++){
            l[i] = new LinkedList<Integer>();
        }
        
        Node node;
        for(int i=1;i<=m;i++){
            luckup[i] = new Node(i);
            while(!l[a[i]].isEmpty()){
                node = getNode(l[a[i]].poll());
                node.next = i;
                getNode(i).children.add(node.id);
            }
            
            l[next[a[i]]].add(i);
        }
        
    }
    
    static int[] remplir(int m,int n){
        int[] s = new int[m+1];
        Arrays.fill(s,-1);
        
        LinkedList<Integer>[] al = new LinkedList[m+1];
        Node node;
        for(int i=1;i<=m;i++){
            al[i-1] = new LinkedList<Integer>();
            node = getNode(i);
            for(int u:node.children){
                al[i-1].add(u-1);
            }
        }
        al[m] = new LinkedList<Integer>();
        for(int i=1;i<=m;i++){
            node = getNode(i);
            if(node.next==0){
                al[m].add(i-1);
            }
        }
        
        
        SparseTree st = new SparseTree(m+1,m,al);
        int id;
        for(int i=0;i<m;i++){
            id = st.getParent(i,n-1);
            if(id==-1 || id==m) continue;
            node = getNode(id);
            s[i+1] = id+1;
        }
        
        
        
        int min = -1;
        for(int i=m;i>=1;i--){
            if(min==-1 && s[i]==-1) continue;
            if(min==-1){
                min = s[i];
                continue;
            } 
            if(s[i]==-1) s[i] = min;
            else s[i] = Math.min(min,s[i]);
            min = Math.min(min,s[i]);
            
        }
        return s;
    }
    
    public static void main(String[] args) throws Exception{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        int q = Integer.parseInt(st.nextToken());
        int[] p = new int[n];
        int[] a = new int[m+1];
        int l,r;
        luckup = new Node[m+1];
        st = new StringTokenizer(br.readLine());
        for(int i=0;i<n;i++) p[i] = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(br.readLine());
        for(int i=1;i<=m;i++) a[i] = Integer.parseInt(st.nextToken());
        next = new int[n+1];
        for(int i=0;i<n;i++){
            next[p[i]] = p[(i+1)%n];
        }
        int[] s;
        
        if(n==1){
            s = new int[m+1];
            for(int i=1;i<=m;i++) s[i] = i;
        }else{
            build(a,m,n);
            s = remplir(m,n);
        }
        
        for(int i=0;i<q;i++){
            st = new StringTokenizer(br.readLine());
            l = Integer.parseInt(st.nextToken());
            r = Integer.parseInt(st.nextToken());
            if(s[l]==-1) out.print("0");
            else if(s[l]<=r) out.print("1");
            else out.print("0");
        }
        out.println("");
        out.flush();
        
    }
}