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.
/*
 ID: tommatt1
 LANG: JAVA
 TASK: 
*/
import java.util.*;
import java.io.*;
public class cf1142b{

	public static void main(String[] args)throws IOException {
		BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		//BufferedReader bf=new BufferedReader(new FileReader("cf1142b.in"));
		//PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("cf1142b.out")));
		StringTokenizer st=new StringTokenizer(bf.readLine());
		int n=Integer.parseInt(st.nextToken());
		int m=Integer.parseInt(st.nextToken());
		int q=Integer.parseInt(st.nextToken());
		int[] p=new int[n+1];
		int[] a=new int[m+1];
		int[] min=new int[m+1];
		int[] lst=new int[n+1];
		int[] prev=new int[n+1];
		int[][] par=new int[m+1][18];
		st=new StringTokenizer(bf.readLine());
		for(int i=1;i<=n;i++) {
			p[i]=Integer.parseInt(st.nextToken());
			prev[p[i]]=p[i-1];
		}
		prev[p[1]]=p[n];
		st=new StringTokenizer(bf.readLine());
		for(int i=1;i<=m;i++) {
			a[i]=Integer.parseInt(st.nextToken());
			lst[a[i]]=i;
			par[i][0]=lst[prev[a[i]]];
			min[i]=(int)2e5+5;
			for(int j=1;j<=17;j++) {
				par[i][j]=par[par[i][j-1]][j-1];
			}
			int z=i;
			for(int j=0;j<=17;j++) {
				if((n-1>>j&1)>0) z=par[z][j];
			}
			min[z]=Math.min(min[z], i);
		}
		for(int i=m-1;i>=1;i--) {
			min[i]=Math.min(min[i], min[i+1]);
		}
		for(int i=0;i<q;i++) {
			st=new StringTokenizer(bf.readLine());
			int a1=Integer.parseInt(st.nextToken());
			int a2=Integer.parseInt(st.nextToken());
			if(min[a1]<=a2) out.print(1);
			else out.print(0);
		}
		out.println("");
		out.close();
	}

}


