At the University of Squirreloo, first-year squirrels in the math faculty have to take MATH 137: calculus, everyone's favourite branch of math! In this course they learn about *convergent* sequences, where values in a sequence get arbitrarily close to a limit. However, said sequences are infinite, and infinity is a concept too difficult to tackle immediately for our young squirrels, so they'll first discuss sequences of finite length - namely, an array of length . We'll say an array converges to a limit with an accuracy of if there exists a suffix of such that all elements in differ from by at most . Given an array of length , the squirrels are given assignment questions of the form , and are tasked to determine whether or not converges to with an accuracy of , and if so, to find the length of the **longest suffix** of that fulfills the definition above.

#### Constraints

**For this problem, you will be required to pass all the samples in order to receive any points. In addition, you must pass all previous subtasks to earn points for a specific subtask.**

For all subtasks:

for all

##### Subtask 1 [18%]

##### Subtask 2 [82%]

No additional constraints.

#### Input Specification

On the first line will be two integers and , the length of the array and the number of assignment questions respectively.

The second line will contain integers , the array .

The following lines will each contain two integers and , the limit and accuracy to test for on the assignment question.

#### Output Specification

**This problem is graded with an identical checker. This includes whitespace characters. Ensure that every line of output is terminated with a \n character and that there are no trailing spaces.**

Output lines. The line should contain the length of the longest suffix of such that all elements in the suffix differ from by at most . If such a suffix does not exist, output .

#### Sample Input 1

```
8 5
1 5 4 6 -2 3 4 0
0 4
2 2
1 5
-1 0
5 5
```

#### Sample Output 1

```
4
3
8
0
3
```

#### Sample Input 2

```
5 5
1 2 3 4 5
5 1
4 1
2 2
2 3
1 5
```

#### Sample Output 2

```
2
3
0
5
5
```

## Comments

off-by-ones make my brain hurt