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 <bits/stdc++.h>

using namespace std;

typedef pair<int,int> P;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vll;

// #define int long long
#define pb push_back
#define mp make_pair
#define eps 1e-9
#define INF 2000000000
#define LLINF 10000000000000ll
#define fi first
#define sec second
#define all(x) (x).begin(),(x).end()
#define sq(x) ((x)*(x))
#define dmp(x) cerr << #x << ": " << x << endl;

template<class T> void chmin(T& a,const T& b){if(a>b)a=b;}
template<class T> void chmax(T& a,const T& b){if(a<b)a=b;}
template<class T>
using MaxHeap = priority_queue<T>;
template<class T>
using MinHeap = priority_queue<T,vector<T>,greater<T> >;
template<class T,class U>
ostream& operator << (ostream& os,const pair<T,U>& p){
  os << p.fi << ',' << p.sec; return os;
}
template<class T,class U>
istream& operator >> (istream& is,pair<T,U>& p){
  is >> p.fi >> p.sec; return is;
}
template<class T>
ostream& operator << (ostream &os,const vector<T> &vec){
  for(int i=0;i<vec.size();i++){
    os << vec[i];
    if(i+1<vec.size())os << ' ';
  }
  return os;
}
template<class T>
istream& operator >> (istream &is,vector<T>& vec){
  for(int i=0;i<vec.size();i++)is >> vec[i];
  return is;
}
void fastio(){
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout<<fixed<<setprecision(20);
}

namespace Math{
  template<int MOD> // if inv is needed, this shold be prime.
  struct ModInt{
    ll val;
    ModInt():val(0ll){}
    ModInt(const ll& v):val(((v%MOD)+MOD)%MOD){}
    ModInt pow(ModInt a,ll x){
      ModInt res = ModInt(1ll);
      while(x){
        if(x&1)res *= a;
        x >>= 1;
        a = a*a;
      }
      return res;
    }
    bool operator==(const ModInt& x)const{return val==x.val;}
    bool operator!=(const ModInt& x)const{return !(*this==x);}
    bool operator<(const ModInt& x)const{return val<x.val;}
    bool operator>(const ModInt& x)const{return val>x.val;}
    bool operator>=(const ModInt& x)const{return !(*this<x);}
    bool operator<=(const ModInt& x)const{return !(*this>x);}
    ModInt& operator+=(const ModInt& x){if((val+=x.val)>=MOD)val-=MOD;return *this;}
    ModInt& operator-=(const ModInt& x){if((val+=MOD-x.val)>=MOD)val-=MOD;return *this;}
    ModInt& operator*=(const ModInt& x){(val*=x.val)%=MOD;return *this;}
    ModInt operator+(const ModInt& x)const{return ModInt(*this)+=x;}
    ModInt operator-(const ModInt& x)const{return ModInt(*this)-=x;}
    ModInt operator*(const ModInt& x)const{return ModInt(*this)*=x;}
    friend istream& operator>>(istream&i,ModInt& x){ll v;i>>v;x=v;return i;}
    friend ostream& operator<<(ostream&o,const ModInt& x){o<<x.val;return o;}
  };
  constexpr int MOD = 1e9+7;
  using mint = ModInt<MOD>;
  vector<mint> inv,fac,facinv;
  // notice: 0C0 = 1 
  ModInt<MOD> nCr(int n,int r){
    assert(!(n<r));
    assert(!(n<0||r<0));
    return fac[n]*facinv[r]*facinv[n-r];
  }
  void init(int SIZE){
    fac.resize(SIZE+1);
    inv.resize(SIZE+1);
    facinv.resize(SIZE+1);
    fac[0] = inv[1] = facinv[0] = mint(1ll);
    for(int i=1;i<=SIZE;i++)fac[i]=fac[i-1]*mint(i);
    for(int i=2;i<=SIZE;i++)inv[i]=mint(0ll)-mint(MOD/i)*inv[MOD%i];
    for(int i=1;i<=SIZE;i++)facinv[i]=facinv[i-1]*inv[i];
    return;
  }
}

namespace DS{
  template<class T>
  struct RangeSum{
    vector<T> vec;
    RangeSum(){}
    RangeSum(vector<T> elems):vec(elems){
      for(int i=1;i<vec.size();i++){
        vec[i] += vec[i-1];
      }
    }
    T sum(int l,int r){
      if(l>r)return T(0);
      if(l==0)return vec[r];
      else return vec[r]-vec[l-1];
    }
  };
  template<class T,int N>
  struct BIT{
    vector<T> bit;
    BIT(){
      bit = vector<T>(N+1,T(0));
    }
    void add(int i,T x){
      i++;
      while(i<=N){
        bit[i]+=x;
        i+=i&-i;
      }
      return;
    }
    T sum(int i){
      i++;
      T res = T(0);
      while(i>0){
        res+=bit[i];
        i-=i&-i;
      }
      return res;
    }
    T sum(int l,int r){// [l,r]
      assert(l<=r);
      if(l==0)return sum(r);
      else return sum(r)-sum(l-1);
    }
  };
}
signed main(){
  fastio();
  int x,p;
  cin >> x >> p;
  if(x&1)x++;
  cout << x/2.0*100.0/(double)p << endl;
  return 0;
}