Luke (perhaps Skywalker) is a passionate computer science student. He receives as homework the following task:

Given a sequence of integers, determine if the subsequence from to inclusive is a

Great Sequence. AGreat Sequenceis a sequence whose sum is strictly greater than .

Luke thought this is too easy, so he has thought up a new challenge: he'd like to know if a subsequence is an *Amazing Sequence*. An *Amazing Sequence* is a Great Sequence in which the integers and appear. Given his original sequence, he'd like to answer queries, determining if a subsequence is an Amazing Sequence.

#### Constraints

For all subtasks:

##### Subtask 1 [30%]

##### Subtask 2 [70%]

#### Input Specification

The first line of input will contain the space-separated integers , and . The second line of input will contain space-separated integers representing the sequence. For the last lines, line will contain query in the format , , and .

#### Output Specification

For each query, print `Yes`

if the subsequence is an Amazing Sequence, `No`

otherwise.

#### Sample Input

```
5 6 3
1 3 4 5 6
3 6 2 5
1 4 1 4
5 6 1 3
```

#### Sample Output

```
Yes
Yes
No
```

## Comments

Dropped time limit to 0.2s to kill vectorized cheese.

What is wrong with my program? Second subtask passes