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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class B {

	static int N,M,Q;
	static int[] perm, ar, answers;
	static ArrayList<Query> qsHere[];
	
	static int[][] lift;
	static int[] prevPerm;
	
	public static void main(String[] args) {
		FS in = new FS();
		PrintWriter out = new PrintWriter(System.out);
		N = in.nextInt();
		M = in.nextInt();
		Q = in.nextInt();
		perm = new int[N];
		for(int i = 0; i < N; i++) perm[i] = in.nextInt()-1;
		ar = new int[M];
		for(int i = 0; i < M; i++) ar[i] = in.nextInt()-1;
		
		prevPerm = new int[N];
		for(int i = 0; i < N; i++) {
			prevPerm[perm[i]] = perm[(i-1+N)%N];
		}
		
		qsHere = new ArrayList[M];
		for(int i = 0; i < M; i++) qsHere[i] = new ArrayList<Query>();
		for(int i = 0; i < Q; i++) {
			Query q = new Query(in.nextInt()-1, in.nextInt()-1, i);
			qsHere[q.r].add(q);
		}
		
		
		int log = Integer.numberOfTrailingZeros(Integer.highestOneBit(M))+2;
		lift = new int[M+1][log];
		for(int a[] : lift) Arrays.fill(a, -1);
		
		int lastOcc[] = new int[N];
		Arrays.fill(lastOcc, -1);
		
		for(int i = 0; i < M; i++) {
			lift[i][0] = lastOcc[prevPerm[ar[i]]];
			int cur = lift[i][0];
			
			for(int j = 1; j < log; j++) {
				if(cur == -1) break;
				lift[i][j] = lift[cur][j-1];
				cur = lift[i][j];
			}
			lastOcc[ar[i]] = i;
		}
		
		answers = new int[Q];
		int furthestRight = -1;
		for(int i = 0; i < M; i++) {
			// Process this index
			int left = N-1;
			int cur = i;
			for(int j = log-1; j >= 0; j--) {
				if(cur == -1) break;
				if((1<<j) > left) continue;
				cur = lift[cur][j];
				left -= (1<<j);
			}
			furthestRight = Math.max(furthestRight, cur);
			
			// answer queries here
			for(Query q : qsHere[i]) {
				if(furthestRight >= q.l) answers[q.id] = 1;
				else answers[q.id] = 0;
			}
		}
		
		for(int ii : answers) out.print(ii);
		out.println();
		out.close();
		
	}
	static class Query {
		int l, r, id;
		public Query(int ll, int rr, int ii) {
			l=ll;
			r=rr;
			id=ii;
		}
	}

	static class FS {
		 BufferedReader br;
		 StringTokenizer st;
		 public FS() { br = new BufferedReader(new InputStreamReader(System.in));}
		 String next() {
			 while(st == null || !st.hasMoreElements()) {
				 try {st = new StringTokenizer(br.readLine());}
				 catch(Exception e) { throw null;}
			 }
			 return st.nextToken();
		 }
		 int nextInt() { return Integer.parseInt(next());}
	}
}
