# POJ3069 Saruman's Army

October 17, 2018

## 内容

Status: Draft

今天让我们一起看POJ3069[1]吧。

## Problem

### Description

Saruman the White must lead his army along a straight path from Isengard to Helm’s Deep. To keep track of his forces, Saruman distributes seeing stones, known as palantirs, among the troops. Each palantir has a maximum effective range of R units, and must be carried by some troop in the army (i.e., palantirs are not allowed to “free float” in mid-air). Help Saruman take control of Middle Earth by determining the minimum number of palantirs needed for Saruman to ensure that each of his minions is within R units of some palantir.


### Input

The input test file will contain multiple cases. Each test case begins with a single line containing an integer R, the maximum effective range of all palantirs (where 0 ≤ R ≤ 1000), and an integer n, the number of troops in Saruman’s army (where 1 ≤ n ≤ 1000). The next line contains n integers, indicating the positions x1, …, xn of each troop (where 0 ≤ xi ≤ 1000). The end-of-file is marked by a test case with R = n = −1.


### Output

For each test case, print a single integer indicating the minimum number of palantirs needed.


### Sample Input

0 3
10 20 20
10 7
70 30 1 7 15 20 50
-1 -1


### Sample Output

2
4


## References

• [1] http://poj.org/problem?id=3069