G. Balls and Pockets
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

There is a strip with an infinite number of cells. Cells are numbered starting with $$$0$$$. Initially the cell $$$i$$$ contains a ball with the number $$$i$$$.

There are $$$n$$$ pockets located at cells $$$a_1, \ldots, a_n$$$. Each cell contains at most one pocket.

Filtering is the following sequence of operations:

  • All pockets at cells $$$a_1, \ldots, a_n$$$ open simultaneously, which makes balls currently located at those cells disappear. After the balls disappear, the pockets close again.
  • For each cell $$$i$$$ from $$$0$$$ to $$$\infty$$$, if the cell $$$i$$$ contains a ball, we move that ball to the free cell $$$j$$$ with the lowest number. If there is no free cell $$$j < i$$$, the ball stays at the cell $$$i$$$.

Note that after each filtering operation each cell will still contain exactly one ball.

For example, let the cells $$$1$$$, $$$3$$$ and $$$4$$$ contain pockets. The initial configuration of balls is shown below (underscores display the cells with pockets):

0 1 2 3 4 5 6 7 8 9 ...

After opening and closing the pockets, balls 1, 3 and 4 disappear:

0   2     5 6 7 8 9 ...

After moving all the balls to the left, the configuration looks like this:

0 2 5 6 7 8 9 10 11 12 ...

Another filtering repetition results in the following:

0 5 8 9 10 11 12 13 14 15 ...

You have to answer $$$m$$$ questions. The $$$i$$$-th of these questions is "what is the number of the ball located at the cell $$$x_i$$$ after $$$k_i$$$ repetitions of the filtering operation?"

Input

The first line contains two integers $$$n$$$ and $$$m$$$ — the number of pockets and questions respectively ($$$1 \leq n, m \leq 10^5$$$).

The following line contains $$$n$$$ integers $$$a_1, \ldots, a_n$$$ — the numbers of cells containing pockets ($$$0 \leq a_1 < \ldots < a_n \leq 10^9$$$).

The following $$$m$$$ lines describe questions. The $$$i$$$-th of these lines contains two integers $$$x_i$$$ and $$$k_i$$$ ($$$0 \leq x_i, k_i \leq 10^9$$$).

Output

Print $$$m$$$ numbers — answers to the questions, in the same order as given in the input.

Example
Input
3 15
1 3 4
0 0
1 0
2 0
3 0
4 0
0 1
1 1
2 1
3 1
4 1
0 2
1 2
2 2
3 2
4 2
Output
0
1
2
3
4
0
2
5
6
7
0
5
8
9
10