Problem: Example

Input

100 1 0
50 100


Output

14.57738

Solution (in CPP):

Solution:
//include
//------------------------------------------
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <ctime>
#include <climits>
#include <queue>

using namespace std;

//typedef
//------------------------------------------
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef long long LL;

//container util
//------------------------------------------
#define ALL(a)  (a).begin(),(a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define SZ(a) int((a).size())
#define EACH(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort((c).begin(),(c).end())

//repetition
//------------------------------------------
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)

//constant
//--------------------------------------------
const double EPS = 1e-10;
const double PI  = acos(-1.0);
const double INF = 1e9;

int main(){
  cin.tie(0);
  ios_base::sync_with_stdio(false);

  double D; int N, B;
  cin >> D >> N >> B;
  vector<double> P(N), H(N);
  REP(i,N) cin >> P[i] >> H[i];

  double ans = INF;
  for(int bi=0;bi<=B;++bi){
	double span = D / (bi+1);
	double vy = 0.;
	for(int i=0;i<N;++i){
	  double pos = P[i];
	  while(pos > span) pos -= span;
	  if(pos > span/2) pos = span - pos;
	  double t = pos / span;
	  vy = max(vy, sqrt(H[i] / (2*t*(1. - t))));
	}
	double vx = span / (2*vy);
	if(vx >= vy) ans = sqrt(span);
	ans = min(ans, sqrt(vx*vx+vy*vy));
  }
  cout << fixed << setprecision(9) << ans << endl;

  return 0;
}