Optimal Subsequences (Hard Version)

ID: 5342

Type: Default

3000ms

256MiB

This is the harder version of the problem. In this version, 1 ≤ n, m ≤ 2⋅10^5. You can hack this problem if you locked it. But you can hack the previous problem only if you locked both problems.

You are given a sequence of integers a=[a_1,a_2,...,a_n] of length n. Its subsequence is obtained by removing zero or more elements from the sequence a (they do not necessarily go consecutively). For example, for the sequence a=[11,20,11,33,11,20,11]:

[11,20,11,33,11,20,11], [11,20,11,33,11,20], [11,11,11,11], [20], [33,20] are subsequences (these are just some of the long list);
[40], [33,33], [33,20,20], [20,20,11,11] are not subsequences.

Suppose that an additional non-negative integer k (1 ≤ k ≤ n) is given, then the subsequence is called optimal if:

it has a length of k and the sum of its elements is the maximum possible among all subsequences of length k;
and among all subsequences of length k that satisfy the previous item, it is lexicographically minimal.

Recall that the sequence b=[b_1, b_2, ..., b_k] is lexicographically smaller than the sequence c=[c_1, c_2, ..., c_k] if the first element (from the left) in which they differ less in the sequence b than in c. Formally: there exists t (1 ≤ t ≤ k) such that b_1=c_1, b_2=c_2, ..., b_{t-1}=c_{t-1} and at the same time b_t<c_t. For example:

[10, 20, 20] lexicographically less than [10, 21, 1],
[7, 99, 99] is lexicographically less than [10, 21, 1],
[10, 21, 0] is lexicographically less than [10, 21, 1].

You are given a sequence of a=[a_1,a_2,...,a_n] and m requests, each consisting of two numbers k_j and pos_j (1 ≤ k ≤ n, 1 ≤ pos_j ≤ k_j). For each query, print the value that is in the index pos_j of the optimal subsequence of the given sequence a for k=k_j.

For example, if n=4, a=[10,20,30,20], k_j=2, then the optimal subsequence is [20,30] — it is the minimum lexicographically among all subsequences of length 2 with the maximum total sum of items. Thus, the answer to the request k_j=2, pos_j=1 is the number 20, and the answer to the request k_j=2, pos_j=2 is the number 30.

Input

The first line contains an integer n (1 ≤ n ≤ 2⋅10^5) — the length of the sequence a.

The second line contains elements of the sequence a: integer numbers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).

The third line contains an integer m (1 ≤ m ≤ 2⋅10^5) — the number of requests.

The following m lines contain pairs of integers k_j and pos_j (1 ≤ k ≤ n, 1 ≤ pos_j ≤ k_j) — the requests.

Output

Print m integers r_1, r_2, ..., r_m (1 ≤ r_j ≤ 10^9) one per line: answers to the requests in the order they appear in the input. The value of r_j should be equal to the value contained in the position pos_j of the optimal subsequence for k=k_j.

Examples

Input

3 10 20 10 6 1 1 2 1 2 2 3 1 3 2 3 3

Output

20 10 20 10 20 10

Input

7 1 2 1 3 1 2 1 9 2 1 2 2 3 1 3 2 3 3 1 1 7 1 7 7 7 4

Output

2 3 2 3 2 3 1 1 3

Note

In the first example, for a=[10,20,10] the optimal subsequences are:

for k=1: [20],
for k=2: [10,20],
for k=3: [10,20,10].

inputFormat

Input

The first line contains an integer n (1 ≤ n ≤ 2⋅10^5) — the length of the sequence a.

The second line contains elements of the sequence a: integer numbers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).

The third line contains an integer m (1 ≤ m ≤ 2⋅10^5) — the number of requests.

The following m lines contain pairs of integers k_j and pos_j (1 ≤ k ≤ n, 1 ≤ pos_j ≤ k_j) — the requests.

outputFormat

Output

Examples

Input

3 10 20 10 6 1 1 2 1 2 2 3 1 3 2 3 3

Output

20 10 20 10 20 10

Input

7 1 2 1 3 1 2 1 9 2 1 2 2 3 1 3 2 3 3 1 1 7 1 7 7 7 4

Output

2 3 2 3 2 3 1 1 3

Note

In the first example, for a=[10,20,10] the optimal subsequences are:

for k=1: [20],
for k=2: [10,20],
for k=3: [10,20,10].

样例

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#D6431. Optimal Subsequences (Hard Version)

Optimal Subsequences (Hard Version)