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## Problem Description

7-UP is a game that can be played by a group of *N* children, standing in a circle. Starting from 1, the children take turns shouting the natural numbers in increasing order, going around the circle. For example, in a group of 9 children, the second child will shout 2, 11, 20, 29, and so on. This will go on for exactly *K* rounds, before the children get tired and stop playing.

However, there is a small catch. If the number that a child is supposed to shout out is a multiple of 7 or contains the digit 7, the child would shout "UP!" in place of the number. So, for example, if a child was supposed to shout 17, he would shout "UP!", as 17 contains the digit 7.

You are the *X*th child in a circle with *N* children. Print out exactly *K* lines, detailing what you are supposed to shout during each round of the game.

## Input

The input will contain one line with exactly three integers, *N*, *K* and *X*.

## Output

The output should contain *K* lines, with each line containing either an integer or the string "UP!".

## Limits

For all subtasks: 1 ≤ N, K ≤ 1000, 1 ≤ X ≤ N.

Subtask 1 (13%): N = X = 7.

Subtask 2 (10%): N = X = 1, 1 ≤ K ≤ 10.

Subtask 3 (15%): N = X = 1, 1 ≤ K ≤ 100.

Subtask 4 (22%): N = X = 1.

Subtask 5 (40%): No additional constraints.

## Sample Input

9 10 2

## Sample Output

2 11 20 29 38 UP! UP! 65 UP! 83

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 13 | 5 | 1s | 256MB | Minimum |

2 | 10 | 5 | 1s | 256MB | Minimum |

3 | 15 | 10 | 1s | 256MB | Minimum |

4 | 22 | 15 | 1s | 256MB | Minimum |

5 | 40 | 26 | 1s | 256MB | Minimum |

6 | 0 | 1 | 1s | 256MB | Minimum |

### Judge Compile Command

g++-8 ans.cpp -o 7up -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512