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.*;

public class LynyrdSkynyrd {
	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt(), m=scan.nextInt(), q=scan.nextInt();
		int[] p=new int[n], id=new int[n];
		for(int i=0;i<n;i++) {
			p[i]=scan.nextInt()-1;
			id[p[i]]=i;
		}
		int[] a=new int[m], last=new int[n];
		jump=new int[m][19];
		//jump[i][j]=jump 2^j places back from i
		
		Arrays.fill(last,-1);
		for(int i=0;i<m;i++) {
			a[i]=scan.nextInt()-1;
			int prevind=(id[a[i]]-1+n)%n;
			jump[i][0]=last[p[prevind]];
			last[a[i]]=i;
		}
		for(int i=0;i<m;i++) {
			for(int j=1;j<=18;j++) {
				if(jump[i][j-1]!=-1) {
					jump[i][j]=jump[jump[i][j-1]][j-1];
				}
				else jump[i][j]=-1;
			}
		}
		int[] res=new int[m];
		//res[i]=greatest index l such that there's a cyclic shift somewhere in l to i
		Arrays.fill(res,-1);
		
		for(int i=0;i<m;i++) {
			int lift=walk(i,n-1);
			res[i]=lift;
			if(i>0) res[i]=Math.max(res[i],res[i-1]);
		}
		
		for(int i=0;i<q;i++) {
			int l=scan.nextInt()-1, r=scan.nextInt()-1;
			System.out.print(res[r]>=l?"1":"0");
		}
	}
	static int[][] jump;
	public static int walk(int i, int k) {
		for(int log=18;log>=0;log--) {
			if(i!=-1&&(k&(1<<log))>0) {
				i=jump[i][log];
				k-=(1<<log);
			}
		}
		return i;
	}
}