## MOMOS - FEASTOFPIGS

The pig's are having a feast tonight!! There are *N* momos numbered from 0 to *N-1*. They are all arranged in a row on a table. Also *K* pigs are attending the feast. The *j ^{th}*pig has hunger

*a[j]*. A pig with hunger

*a[j]*only eats all momos with number i such that when

*i*is divided by

*a[j]*, the remainder is 0. For example, if there are 20 momos and a pig has hunger 3, then the pig will eat momos at position 0,3,6,9,12,15,18.

**Once a momo at a particular position is eaten by one pig, it cannot be eaten by a different pig.**

You're task is simple, given the number of momos, and hunger of *K* pigs, find the total number of momos left after the feast.

### Input

The first line of the input contains two integers N and *K*, where *N* is the number of momos and K is the number of pigs. Lines 2,3,...,K+1 describe the hunger of *K* pigs. Line *i+1 (1 ≤ i ≤ K)* contains a single integer representing the hunger of the *i ^{th}* pig(i.e.

*a[i]*).

* *

*It is guaranteed that:*

**Either (1 ≤ N ≤ 10 ^{6} and 1 ≤ K ≤ 100) or (1≤ N ≤ 10^{14} and 1 ≤ K ≤ 20)**

* The hunger of every pig lies between 1 and N.*

* *

*Output*

*Output*

* *

*A line containing a single integer, which is the number of momos left on the table after all pigs have finished eating.*

* *

*Example*

*Example*

* *

Input:20 3 3 6 5Output:11

* *

Added by: | Salil |

Date: | 2020-04-13 |

Time limit: | 1s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All |

Resource: | Inspired from IARCS judge problems |