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 issam{
    public static int n,m,q;
    public static int[] a,b;
    public static int[] dp;
    public static int[] aft;
    public static LinkedList<Integer>[] al;
    public 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;
        }
        int getSameLevelTo(int u,int v){
            if(u==v||depth[u]==depth[v]) return u;
            if(depth[u]<depth[v]) return -1;
            int diff = depth[u] - depth[v]; 
            u = getParent(u,diff);
            return u;
        }
        int lca(int u, int v) { 
            int k = getSameLevelTo(u,v);
            if(k==-1) v = getSameLevelTo(v,u);
            else u = k;
            if (u == v) 
                return u;
            for (int i=19; i>=0; i--) 
                if (dp[i][u] != dp[i][v]){ 
                    u = dp[i][u]; 
                    v = dp[i][v]; 
                } 
          
            return dp[0][u]; 
        }
    }
    public static void main(String[] args) throws Exception{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        PrintWriter out = new PrintWriter(System.out);
        n = Integer.parseInt(st.nextToken());
        m = Integer.parseInt(st.nextToken());
        q = Integer.parseInt(st.nextToken());
        al = new LinkedList[m+1];
        boolean[] ok = new boolean[m];
        Arrays.fill(ok,true);
        for(int i=0;i<=m;i++) al[i] = new LinkedList<Integer>();
        a = new int[n];
        b = new int[m];
        aft = new int[n];
        st = new StringTokenizer(br.readLine());
        for(int i=0;i<n;i++){
            int v = Integer.parseInt(st.nextToken())-1;
            a[i] = v;
        }
        for(int i=0;i<n-1;i++){
            aft[a[i]] = a[i+1];
        }
        aft[a[n-1]] = a[0];
        st = new StringTokenizer(br.readLine());
        dp = new int[m];
        Arrays.fill(dp,-1);
        for(int i=0;i<m;i++){
            int v = Integer.parseInt(st.nextToken())-1;
            b[i] = v;
        }
        int[] tab = new int[n];
        Arrays.fill(tab,-1);
        for(int i=m-1;i>=0;i--){
            int k = b[i];
            int p = aft[k];
            if(tab[p]!=-1) {
                al[tab[p]].add(i);
                ok[i] = false;
            }
            tab[k] = i;
        }
        for(int i=0;i<m;i++){
            if(ok[i]) al[m].add(i);
        }
        SparseTree sp = new SparseTree(m+1,m,al);
        for(int i=0;i<m;i++){
            dp[i] = sp.getParent(i,n-1);
            if(dp[i]==m) dp[i] = -1;
        }
        for(int i=m-2;i>=0;i--){
            if(dp[i]==-1) dp[i] = dp[i+1];
            else if(dp[i+1]==-1) continue;
            else dp[i] = Math.min(dp[i],dp[i+1]);
        }
        for(int i=0;i<q;i++){
            st = new StringTokenizer(br.readLine());
            int l = Integer.parseInt(st.nextToken())-1;
            int r = Integer.parseInt(st.nextToken())-1;
            if(dp[l]==-1||dp[l]>r) out.print("0");
            else out.print("1");
        }
        out.println("");
        out.flush();
    }
}










