Naofumi is exploring a magical maze! The maze is a 2-D array with pillars. The height of each pillar is generated using two arrays and , each of size . Specifically, the height of the pillar at row and column , pillar , would be . A path in this maze is defined as a sequence of pillars where every successive pillar is below or to the right of the previous pillar (i.e. only moving down or to the right). A valid path is defined as a path where the height of each pillar in the path is . To help him reduce the height of the pillars, Naofumi has a magical modulus spray, allowing him to reduce the height of each pillar to , where is any prime number Naofumi chooses. Being the observant person he is, Naofumi has queries containing integers . For each query, he wants you to find out the maximum prime he can choose such that there is a valid path from to , or determine that it is impossible to create a valid path. Note that he does not actually use the spray after you answer a query. Can you help him find these values?

#### Input Specification

The first line will contain integers and , representing the dimensions of the grid and the number of queries.

The second line will contain integers , representing the array .

The third line will contain integers , representing the array .

The next lines will each contain integers , representing a query from to .

#### Output Specification

The output should contain integers, each on a separate line, representing the maximum prime that can be used to create a valid path for the corresponding query. If no such exists, print `-1`

.

#### Constraints

##### Subtask 1 [20%]

##### Subtask 2 [80%]

No additional constraints.

#### Sample Input

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

#### Sample Output

```
2
3
-1
```

#### Visualization of Sample Input

3 | 4 | 2 | 6 | 5 | |
---|---|---|---|---|---|

2 | 6 | 8 | 4 | 12 | 10 |

3 | 9 | 12 | 6 | 18 | 15 |

1 | 3 | 4 | 2 | 6 | 5 |

4 | 12 | 16 | 8 | 24 | 20 |

3 | 9 | 12 | 6 | 18 | 15 |

## Comments

It is a bit unclear but Naofumi can only use 1 value of per query.