Problem: Aoki is in search of Takahashi, who is missing in a one-dimentional world. Initially, the coordinate of Aoki is 0, and the coordinate of Takahashi is known to be x, but his coordinate afterwards cannot be known to Aoki.

Time is divided into turns. In each turn, Aoki and Takahashi take the following actions simultaneously:

* Let the current coordinate of Aoki be a, then Aoki moves to a coordinate he selects from a-1, a and a+1.

* Let the current coordinate of Takahashi be b, then Takahashi moves to the coordinate b-1 with probability of p percent, and moves to the coordinate b+1 with probability of 100-p percent.




When the coordinates of Aoki and Takahashi coincide, Aoki can find Takahashi. When they pass by each other, Aoki cannot find Takahashi.

Aoki wants to minimize the expected number of turns taken until he finds Takahashi. Find the minimum possible expected number of turns.

Constraints

* 1 ≦ x ≦ 1,000,000,000
* 1 ≦ p ≦ 100
* x and p are integers.

Input

The input is given from Standard Input in the following format:


x
p


Output

Print the minimum possible expected number of turns. The output is considered correct if the absolute or relative error is at most 10^{-6}.

Examples

Input

3
100


Output

2.0000000


Input

6
40


Output

7.5000000


Input

101
80


Output

63.7500000

Solution (in CPP):

Solution:
#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <set>
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <cstdio>
#include <cstring>
#include <iterator>
#include <bitset>
#include <unordered_set>
#include <unordered_map>
#include <fstream>
#include <iomanip>
#include <cassert>
#include <utility>
#include <memory>
#include <functional>
#include <deque>
#include <cctype>
#include <ctime>
#include <numeric>
#include <list>
#include <iomanip>

#if __cplusplus >= 201103L
#include <array>
#include <tuple>
#include <initializer_list>
#include <forward_list>

#define cauto const auto&
#else

#endif

using namespace std;


typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

typedef vector<int> vint;
typedef vector<vector<int> > vvint;
typedef vector<long long> vll;
typedef vector<vector<long long> > vvll;

#define VV(T) vector<vector< T > >

template <class T>
void initvv(vector<vector<T> > &v, int a, int b, const T &t = T()){
    v.assign(a, vector<T>(b, t));
}

template <class F, class T>
void convert(const F &f, T &t){
    stringstream ss;
    ss << f;
    ss >> t;
}

#define GET_MACRO(_1, _2, _3, NAME, ...) NAME
#define _rep(i,n) _rep2((i),0,(n))
#define _rep2(i,a,b) for(int i=(a);i<(b);++i)
#define rep(...) GET_MACRO(__VA_ARGS__, _rep2, _rep)(__VA_ARGS__)
#define ALL(v) (v).begin(),(v).end()
#define PB push_back
#define fi first
#define se second
#define mkp make_pair
#define DEBUG
#ifdef DEBUG
#define dump(x)  cout << #x << " = " << (x) << endl;
#define debug(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;
#else
#define dump(x) 
#define debug(x) 
#endif

#define MOD 1000000007LL
#define EPS 1e-8
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
#define maxs(x,y) x=max(x,y)
#define mins(x,y) x=min(x,y)

void mainmain(){
	ll _x;
	cin>>_x;
	double x=_x;
	double p;
	cin>>p;
	p = p/100;
	double ans;
	if(_x%2==0){
		ans = 1/p*x/2;
	}
	else{
		ans = p*(1/p*(x-1)/2) + (1-p)*(1/p*(x+1)/2);
		ans+=1;
	}
	cout<<ans<<endl;
}


signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout<<fixed<<setprecision(20);
    mainmain();
}