A16200 | Iva & Pav
时间限制1s
内存限制256MB
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题目描述
Iva and Pav are a famous Serbian competitive programming couple. In Serbia, they call Pav "papuca" and that's why he will make all of Iva's wishes come true.
Iva gave Pav an array $a$ of $n$ elements.
Let's define $f(l, r) = a_l \ \& \ a_{l+1} \ \& \dots \& \ a_r$ (here $\&$ denotes the [bitwise AND operation](http://tiny.cc/bitwise_and)).
Note that $f(l, r)$ is not defined when $l>r$ .
Iva also gave Pav $q$ queries.
Each query consists of 2 numbers, $k$ and $l$ , and she wants Pav to find the largest index $r$ ( $l \le r \le n$ ), such that $f(l, r) \ge k$ .
Pav wants to solve this problem fast because he doesn't want to upset Iva. He needs your help.
Iva gave Pav an array $a$ of $n$ elements.
Let's define $f(l, r) = a_l \ \& \ a_{l+1} \ \& \dots \& \ a_r$ (here $\&$ denotes the [bitwise AND operation](http://tiny.cc/bitwise_and)).
Note that $f(l, r)$ is not defined when $l>r$ .
Iva also gave Pav $q$ queries.
Each query consists of 2 numbers, $k$ and $l$ , and she wants Pav to find the largest index $r$ ( $l \le r \le n$ ), such that $f(l, r) \ge k$ .
Pav wants to solve this problem fast because he doesn't want to upset Iva. He needs your help.
输入格式
The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases.
The first line of each test case contains a single integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the length of array $a$ .
The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^9$ ) — the elements of array $a$ .
The third line of each test case contains a single integer $q$ ( $1 \le q \le 10^5$ ) — the number of queries Iva gave Pav.
The next $q$ lines of each test case contains two numbers, $l$ and $k$ ( $1 \le l \le n$ , $1 \le k \le 10^9$ ) — the left bound for the subsegment, and the integer $k$ described in statement.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ . Also, it is guaranteed that the sum of $q$ over all test cases does not exceed $2 \cdot 10^5$ .
The first line of each test case contains a single integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the length of array $a$ .
The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^9$ ) — the elements of array $a$ .
The third line of each test case contains a single integer $q$ ( $1 \le q \le 10^5$ ) — the number of queries Iva gave Pav.
The next $q$ lines of each test case contains two numbers, $l$ and $k$ ( $1 \le l \le n$ , $1 \le k \le 10^9$ ) — the left bound for the subsegment, and the integer $k$ described in statement.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ . Also, it is guaranteed that the sum of $q$ over all test cases does not exceed $2 \cdot 10^5$ .
输出格式
For each query output maximal index $r$ ( $l \le r \le n$ ) such that $a_l \ \& \ a_{l+1} \ \& \dots \& \ a_r \ \ge \ k$ .
If such $r$ doesn't exist, output $-1$ .
If such $r$ doesn't exist, output $-1$ .
输入输出样例
输入 #1
3 5 15 14 17 42 34 3 1 7 2 15 4 5 5 7 5 3 1 7 4 1 7 5 7 2 3 2 2 7 19 20 15 12 21 7 11 4 1 15 4 4 7 12 5 7
输出 #1
2 -1 5 1 5 2 2 2 6 -1 5
In the first test case $n=5$ , and the array $a = [15, 14, 17, 42, 34]$
The first query asks for the biggest index $r$ such that the $f(1, r) \ge 7$ .
$f(1,1) = 15, \ f(1, 2) = 14, \ f(1,3)=0 \ f(1, 4)=0 \ f(1, 5)=0$ , so $r=2$ is the answer.
The second query asks for $f(2, r) \ge 15$ . Since such $r$ doesn't exist, the answer is $-1$ .
The third query asks for $f(4, r) \ge 5$ . $f(4, 4) = 42, \ f(4, 5) = 34$ , so $r=5$ is the answer.
In the second test case $n=5$ , and the array $a= [7, 5, 3, 1, 7]$ .
For the first query, $f(1, r) \ge 7$ .
$f(1, 1)=7, \ f(1, 2)=5, \ f(1, 3) = 1, \ f(1,4) = 1, \ f(1, 5)=1$ , so the answer to this query is $1$ .
For the second query, $f(5, r) \ge 7$ .
$f(5, 5) = 7$ , so the answer is $5$ .
For the third query, $f(2, r) \ge 3$ .
$f(2, 2) = 5, \ f(2, 3) = 1, \ f(2, 4) = 1, \ f(2, 5) = 1$ , so the answer is $2$ .
The first query asks for the biggest index $r$ such that the $f(1, r) \ge 7$ .
$f(1,1) = 15, \ f(1, 2) = 14, \ f(1,3)=0 \ f(1, 4)=0 \ f(1, 5)=0$ , so $r=2$ is the answer.
The second query asks for $f(2, r) \ge 15$ . Since such $r$ doesn't exist, the answer is $-1$ .
The third query asks for $f(4, r) \ge 5$ . $f(4, 4) = 42, \ f(4, 5) = 34$ , so $r=5$ is the answer.
In the second test case $n=5$ , and the array $a= [7, 5, 3, 1, 7]$ .
For the first query, $f(1, r) \ge 7$ .
$f(1, 1)=7, \ f(1, 2)=5, \ f(1, 3) = 1, \ f(1,4) = 1, \ f(1, 5)=1$ , so the answer to this query is $1$ .
For the second query, $f(5, r) \ge 7$ .
$f(5, 5) = 7$ , so the answer is $5$ .
For the third query, $f(2, r) \ge 3$ .
$f(2, 2) = 5, \ f(2, 3) = 1, \ f(2, 4) = 1, \ f(2, 5) = 1$ , so the answer is $2$ .
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评测结果：Accepted