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.
#! /usr/bin/python

from collections import deque

n, m, q = [int(inp) for inp in raw_input().split()]

p = [int(inp) for inp in raw_input().split()]
nxt = [-1 for _ in xrange(n + 1)]
for i in range(n):
	nxt[p[i]] = p[(i + 1) % n]
a = [int(inp) for inp in raw_input().split()]

stepTo = [m for _ in xrange(m)]

last = [-1] + [m for i in xrange(n)]
for i in xrange(m - 1, -1, -1):
	last[a[i]] = i
	stepTo[i] = last[nxt[a[i]]]

def stepMult(step1, step2):
	return [step1[x] if x < len(step1) else len(step1) for x in step2]

def stepPwr(step, p):
	res = range(len(step))
	while p > 0:		
		if p % 2 == 1:
			res = stepMult(res, step)
		step = stepMult(step, step)
		p /= 2
	return res

stepN = stepPwr(stepTo, n - 1)

curMin = m
for i in xrange(m - 1, -1, -1):
	if stepN[i] < curMin:
		curMin = stepN[i]
	stepN[i] = curMin

res = []
for _ in xrange(q):
	l, r = [int(inp) for inp in raw_input().split()]
	l -= 1
	r -= 1

	if stepN[l] <= r:
		res += ['1']
	else:
		res += ['0']

print "".join(res)



