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.*;
import java.text.*;
import java.util.*;
import java.math.*;
public class E {
	public static void main(String[] args) throws Exception {
		new E().run();
	}
	public void run() throws Exception {
		FastScanner f = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		int n = f.nextInt(), m = f.nextInt(), q = f.nextInt();
		int[] map = new int[n];
		for(int i = 0; i < n; i++) map[f.nextInt()-1] = i;
		int[] arr = new int[m];
		int[] prev = new int[n];
		Arrays.fill(prev, m);
		int[][] aft = new int[m+1][20];
		for(int i = 0; i < m; i++)
			arr[i] = map[f.nextInt()-1];
		for(int i = m-1; i >= 0; i--) {
			aft[i][0] = prev[(arr[i]+1)%n];
			prev[arr[i]] = i;
		}
		Arrays.fill(aft[m], m);
		ans = new int[m];
		for(int i = m-1; i >= 0; i--) {
			for(int j = 1; j < 20; j++)
				aft[i][j] = aft[aft[i][j-1]][j-1];
			int j = i;
			int v = n-1;
			for(int b = 19; b >= 0; b--)
				if(v >= (1 << b)) {
					j = aft[j][b];
					v -= 1 << b;
				}
			ans[i] = j;
		}
		seg = new int[4*m];
		init(0, 0, m);
		while(q-->0) {
			int l = f.nextInt()-1, r = f.nextInt();
			out.print(query(0, 0, m, l, r) < r ? 1 : 0);
		}
		out.println();
		out.flush();
	}
	int[] ans;
	int[] seg;
	public void init(int i, int l, int r) {
		if(l == r-1) seg[i] = ans[l];
		else {
			int m = (l+r)/2;
			init(2*i+1,l,m);
			init(2*i+2,m,r);
			seg[i] = Math.min(seg[2*i+1], seg[2*i+2]);
		}
	}
	public int query(int i, int l, int r, int ql, int qr) {
		if(ql < l) ql = l;
		if(qr > r) qr = r;
		if(ql >= r || qr <= l) return 2147483647;
		if(ql == l && qr == r) return seg[i];
		int m = (l+r)/2;
		return Math.min(query(2*i+1, l, m, ql, qr), query(2*i+2, m, r, ql, qr));
	}
///
	static class FastScanner {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
		public FastScanner() { reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch(IOException e) {
				throw new RuntimeException(e);
			}
		}
	}
}
