Macarie has received a new problem as part of his informatics assignment, and here is its statement:

We are given an array $A$ with $N$ positive integers. Let's consider the increasing array $D$ made of all positive divisors, not necessarily distinct of the values from $A$. As an example, for $N=4$ and $A=(6, 2, 3, 2)$, we have the array $D=(1,1,1,1,2,2,2,3,3,6)$.

## Task

Given an array $Poz$ made of $Q$ positive integers, representing positions from $D$, find for each of the values, the value at the respective position from the array $D$.

## Input data

The first line of the input file `macarie.in`

contains the integers $N$ and $Q$.

The second line of the input contains $N$ positive integers, representing the values from $A$.

The third line has $Q$ positive integers, representing the values from $Poz$. The numbers on the same line are separated by singular spaces.

## Output data

The first line of the output file `macarie.out`

contains $Q$ positive integers, separated by spaces, representing the values from $D$, in order in which the positions show up in $Poz$.

## Constraints and clarifications

- $1\leq N \leq 1 \ 000 \ 000$, $1\leq Q \leq 100 \ 000$;
- The arrays $A$, $D$ and $Poz$ are indexed from $1$.
- $1 \leq A_i \leq 1 \ 000 \ 000$ for $1 \leq i \leq N$. The values from $A$ are not necessarily distinct.
- $1 \leq Poz_i \leq |D|$ for $1 \leq i \leq Q$, wher $|D|$ is the length of $D$.

# | Score | Constraints |
---|---|---|

1 | 23 | All input values are $\leq 1 \ 000$ |

2 | 18 | All values $A_i$ are prime numbers |

3 | 23 | $N \leq 10 \ 000$, $Poz_i \leq 2 \ 000 \ 000$ |

4 | 15 | $Poz_i\leq 2 \ 000 \ 000$ |

5 | 21 | No additional constraints. |

## Example 1

`macarie.in`

```
4 5
32 42 49 21
2 5 9 7 17
```

`macarie.out`

```
1 2 4 3 21
```

### Explanation

$N = 4$ and $Q = 5$. $A = (32, 42, 49, 21)$ and $D = (1, \underline{1}, 1, 1, \underline{2}, 2, \underline{3}, 3, \underline{4}, 6, 7, 7, 7, 8, 14, 16, \underline{21}, 21, 32, 42, 49)$.

## Example 2

`macarie.in`

```
5 4
24 56 8 490 28
35 25 28 38
```

`macarie.out`

```
70 12 14 490
```

### Explanation

$N = 5$, $Q = 4$ and $D[35] = 70$, $D[25] = 12$, $D[28] = 14$, $D[38] = 490$.