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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.util.function.BinaryOperator;

public class Main {

	static PrintWriter out;
	static InputReader ir;

	static void solve() {
		int n = ir.nextInt();
		int m = ir.nextInt();
		int q = ir.nextInt();
		int[] p = ir.nextIntArray(n);
		int[] a = ir.nextIntArray(m);
		int[] np = new int[n + 1];
		for (int i = 0; i < n; i++) {
			np[p[i]] = p[(i + 1) % n];
		}
		int[][] nxt = new int[20][m];
		int[] pos = new int[n + 1];
		Arrays.fill(pos, -1);
		for (int i = m - 1; i >= 0; i--) {
			nxt[0][i] = pos[np[a[i]]];
			pos[a[i]] = i;
		}
		for (int i = 0; i < 19; i++) {
			for (int j = 0; j < m; j++) {
				if (nxt[i][j] < 0) {
					nxt[i + 1][j] = -1;
				} else {
					nxt[i + 1][j] = nxt[i][nxt[i][j]];
				}
			}
		}
		long[] last = new long[m];
		long INF = 1L << 60;
		for (int i = 0; i < m; i++) {
			int cur = i;
			for (int j = 19; j >= 0; j--) {
				if (((n - 1) & 1 << j) != 0) {
					cur = nxt[j][cur];
					if (cur < 0)
						break;
				}
			}
			if (cur >= 0) {
				last[i] = cur;
			} else {
				last[i] = INF;
			}
		}
		StringBuilder sb = new StringBuilder();
		BinaryOperator<Long> f = (A, B) -> (long) Math.min(A, B);
		SegmentTree st = new SegmentTree(last, f, INF);
		while (q-- > 0) {
			int l = ir.nextInt() - 1;
			int r = ir.nextInt() - 1;
			sb.append(st.query(l, r + 1) <= r ? 1 : 0);
		}
		out.println(sb);
	}

	static class SegmentTree {

		BinaryOperator<Long> f;
		int n;
		long[] seg;
		long e;

		public SegmentTree(int nn, BinaryOperator<Long> f, long e) {
			this.f = f;
			this.e = e;
			n = 1;
			while (n < nn)
				n <<= 1;
			seg = new long[n * 2 - 1];
			Arrays.fill(seg, e);
		}

		public SegmentTree(long[] a, BinaryOperator<Long> f, long e) {
			this.f = f;
			this.e = e;
			n = 1;
			while (n < a.length)
				n <<= 1;
			seg = new long[n * 2 - 1];
			Arrays.fill(seg, e);
			for (int i = 0; i < a.length; i++)
				seg[i + n - 1] = a[i];
			for (int i = n - 2; i >= 0; i--)
				seg[i] = f.apply(seg[i * 2 + 1], seg[i * 2 + 2]);
		}

		public long query(int l, int r) {
			return query(l, r, 0, 0, n);
		}

		private long query(int a, int b, int k, int l, int r) {
			if (a <= l && r <= b)
				return seg[k];
			if (r <= a || b <= l)
				return e;
			long vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
			long vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
			return f.apply(vl, vr);
		}

		void update(int i, int x) {
			i += n - 1;
			seg[i] = x;
			while (i > 0) {
				i = (i - 1) / 2;
				seg[i] = f.apply(seg[i * 2 + 1], seg[i * 2 + 2]);
			}
		}
	}

	public static void main(String[] args) {
		ir = new InputReader(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}

	static class InputReader {

		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;

		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}

		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}

		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}

		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}

		public boolean hasNext() {
			skip();
			return hasNextByte();
		}

		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}

	static void tr(Object... o) {
		out.println(Arrays.deepToString(o));
	}
}