【CF Round 434 B. Which floor?】
time limit per test 1 second
memory limit per test 256 megabytes
input standard input
output standard output
In a building where Polycarp lives there are equal number of flats on each floor. Unfortunately, Polycarp don't remember how many flats are on each floor, but he remembers that the flats are numbered from 1 from lower to upper floors. That is, the first several flats are on the first floor, the next several flats are on the second and so on. Polycarp don't remember the total number of flats in the building, so you can consider the building to be infinitely high (i.e. there are infinitely many floors). Note that the floors are numbered from 1.
Polycarp remembers on which floors several flats are located. It is guaranteed that this information is not self-contradictory. It means that there exists a building with equal number of flats on each floor so that the flats from Polycarp's memory have the floors Polycarp remembers.
Given this information, is it possible to restore the exact floor for flat n?
Input
The first line contains two integers n and m (1 ≤ n ≤ 100, 0 ≤ m ≤ 100), where n is the number of the flat you need to restore floor for, and m is the number of flats in Polycarp's memory.
m lines follow, describing the Polycarp's memory: each of these lines contains a pair of integers ki, fi (1 ≤ ki ≤ 100, 1 ≤ fi ≤ 100), which means that the flat ki is on the fi-th floor. All values ki are distinct.
It is guaranteed that the given information is not self-contradictory.
Output
Print the number of the floor in which the n-th flat is located, if it is possible to determine it in a unique way. Print -1 if it is not possible to uniquely restore this floor.
Examples
Input
10 3
6 2
2 1
7 3
Output
4
Input
8 4
3 1
6 2
5 2
2 1
Output
-1
Note
In the first example the 6-th flat is on the 2-nd floor, while the 7-th flat is on the 3-rd, so, the 6-th flat is the last on its floor and there are 3 flats on each floor. Thus, the 10-th flat is on the 4-th floor.
In the second example there can be 3 or 4 flats on each floor, so we can't restore the floor for the 8-th flat.
【翻译】一栋无限高的楼，每一层的房间数相同。现在从一楼开始为房间标号，一层标完才标下一层。给出n条信息和一个目标房间号m,接下来输入n个二元组(k,f)表示有一个编号为k的房间在f层。询问m号房间所在楼层是否确定？确定则输出所在楼层，否则输出-1。
题解：
①设每层楼有x个房间，对于每条信息可以获得一个x的范围。
②最后取n个范围的交集，判断是否是唯一的(l是否等于r)
#include<math.h>
#include<stdio.h>
#include<algorithm>
#define L(i) ceil(1.0*k[i]/f[i])
#define go(i,a,b) for(int i=a;i<=b;i++)
#define R(i) floor(1.0*(k[i]-1)/(f[i]-1))
#define pos(x) (n/x+(n%x!=0))
int n,m,f[102],k[102],l=-1,r=1e9;
int main()
{
scanf("%d%d",&n,&m);
if(n==1){puts("1");return 0;}
go(i,1,m)scanf("%d%d",k+i,f+i),
l=std::max(l,f[i]>1?(int)L(i):k[i]),
r=std::min(r,f[i]>1?(int)R(i):(int)1e9);
printf("%d\n",pos(l)==pos(r)?pos(l):-1);return 0;
}//Paul_Guderian
