Roger has a strange array consisting of elements, each of which is either or . He also has queries, each of the form which means that Roger wants to know whether there exists a subarray where whose sum of elements is exactly .

#### Constraints

In all subtasks

Each element of the array is either or .

##### Subtask 1 [20%]

##### Subtask 2 [80%]

No additional constraints.

#### Input Specification

On the first line, there are two space-separated integers, and , denoting the number of elements in the array and the number of queries.

On the second line, there are space-separated integers, the elements of the array.

On the next lines, there are three space-separated integers, , denoting a query.

#### Output Specification

Output lines, where the -th line is `YES`

if there exists a subarray satisfying the conditions of Roger's -th query, or `NO`

otherwise.

#### Sample Input

```
7 3
1 2 2 1 1 2 1
2 4 3
1 7 8
2 5 7
```

#### Sample Output

```
YES
YES
NO
```

## Comments