##### National Olympiad in Informatics, China, 2014

Little H has recently been studying randomized algorithms. Randomized
algorithms often use random number generation functions (e.g. `random`

from Pascal and `rand`

from C/C++) to obtain their randomness. In
reality, random number functions are not truly "random." Instead, they
work off of some specific algorithms.

As such, the following recursive quadratic polynomial is one method:

The algorithm selects nonnegative integers , , , , and as its seed values and uses the following recursive calculations to generate a random number.

For any , .

This way, a sequence of nonnegative integers of arbitrary length can be obtained. Typically, we can consider this sequence to be random. Using the sequence , we can use the following algorithm to produce , a random permutation of the numbers to .

- Initialize to the sequence of integers from to .
- Perform swaps on the sequence . The -th swap will swap the value of with the value of .

Outside of this base number of swaps, little H has made **an
additional** swaps. For the -th additional swap, little H will
choose two positions and and swap the values of
and .

To check the effectiveness of the random permutation generator, little H designed the following problem:

Little H has an row by column grid. She initially follows the above process, producing a random permutation of the integers from to after swaps. Then these values are then placed back into the grid, row for row, column for column. That is, the cell at column of row in the original grid will now take on the value of .

Afterwards, little H wishes to start from the top-left corner of the
grid (i.e. row , column ), **each step moving either right or down
under the precondition that she does not move outside of the grid**, and
reach the bottom-right corner (i.e. row , column ).

Little H writes down the value of every cell she travels through,
**ordered from least to greatest**. This way, for any valid path, little
H can obtain an increasing sequence of length which we
will call the **path sequence**. Little H wishes to know the
**lexicographically smallest** path sequence that she can obtain.

#### Input Specification

Line 1 of input consists of five integers , , , , and
, representing the seed values to little H's random number
generator.

Line 2 of input consists of three integers , , and , indicating
that little H generates a permutation from to to fill her
grid. Also, after little H performs her swaps, she
will perform an additional swaps.

The final lines will each contain two integers and ,
indicating that the -th additional swap involves swapping
and .

#### Output Specification

The output should consist of one line containing space-separated positive integers, representing the lexicographically smallest path sequence that little H can obtain.

#### Sample Input 1

```
1 3 5 1 71
3 4 3
1 7
9 9
4 9
```

#### Sample Output 1

`1 2 6 8 9 12`

#### Sample Input 2

```
654321 209 111 23 70000001
10 10 0
```

#### Sample Output 2

`1 3 7 10 14 15 16 21 23 30 44 52 55 70 72 88 94 95 97`

#### Sample Input 3

```
123456 137 701 101 10000007
20 20 0
```

#### Sample Output 3

`1 10 12 14 16 26 32 38 44 46 61 81 84 101 126 128 135 140 152 156 201 206 237 242 243 253 259 269 278 279 291 298 338 345 347 352 354 383 395`

#### Explanation

For sample 1, according to the input seed values, the first 12 random numbers of are:

`9 5 30 11 64 42 36 22 1 9 5 30`

With these 12 random numbers, little H will perform 12 swap operations, yielding the following:

`6 9 1 4 5 11 12 2 7 10 3 8`

After the additional 3 swap operations, little H obtains the final permuted sequence of:

`12 9 1 7 5 11 6 2 4 10 3 8`

This sequence will yield the following grid.

The optimal path sequence is: .

#### Constraints

The constraints of all the test cases are outlined below.

Test Case | , | Other Constraints | |
---|---|---|---|

1 |
| ||

2 | |||

3 | |||

4 | |||

5 | |||

6 | |||

7 | |||

8 | |||

9 | |||

10 |

Problem translated to English by .

## Comments