There is a class of students, numbered through . Every day the teacher of the class has some projects for the students. Each project has to be completed by a team of students within the same day. The projects may have various difficulty. For each project, the teacher knows the exact size of a team that should work on it.

Different students may prefer different team sizes. More precisely, student can only be assigned to a team of size between and inclusive. On each day, a student may be assigned to at most one team. Some students might not be assigned to any teams. Each team will work on a single project.

The teacher has already chosen the projects for each of the next days. For each of these days, determine whether it is possible to assign students to teams so that there is one team working on each project.

#### Example

Suppose there are students and days. The students' constraints on team sizes are given in the table below:

Student | 0 | 1 | 2 | 3 |
---|---|---|---|---|

A | 1 | 2 | 2 | 2 |

B | 2 | 3 | 3 | 4 |

On the first day there are projects. The required team sizes are and . These two teams can be formed by assigning student 0 to a team of size 1 and the remaining three students to a team of size 3.

On the second day there are projects again, but this time the required team sizes are and . In this case it is not possible to form the teams, as there is only one student who can be in a team of size 1.

You are given the description of all students: , , and , as well as a sequence of queries — one about each day. Each question consists of the number of projects on that day and a sequence of length containing the required team sizes. For each question, your program must return whether it is possible to form all the teams.

#### Input Specification

Line of input will contain a single integer , representing the number of students.

Lines will each contain a pair of space-separated integers and , representing the length arrays and , where is the minimum team size for student and is the maximum team size for student .

Line will contain a single integer , representing the number of queries to follow.

Lines will each consists of a query in the format , . represents the number of projects for this day and is an array of length containing the required team size for each of these projects.

#### Output Specification

For each query, output a separate line containing either `1`

if it is possible to form all the required teams, or `0`

otherwise.

#### Sample Input

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

#### Sample Output

```
1
0
```

#### Subtasks

Let us denote by the sum of values of .

subtask | points | Additional Constraints | ||
---|---|---|---|---|

1 | 21 | none | ||

2 | 13 | none | ||

3 | 43 | |||

4 | 23 |

## Comments

Is there a project of size 0?